There were 6.0 roses in the vase. Mary cut some roses from her flower garden. There are now 16.0 roses in the vase. How many roses did she cut? Answer:

41. Kathleen and Glenn decide that this is the year to begin getting serious about saving for their retirement by participating in their employers' 401k plans. As aresult, they each have $3000 of their salary set aside in their qualified plans.
0*0.20 = 800. Answer: $800. b. Joel is under 18 at the end of the year, so he is not eligible for the credit. Answer: $0.

NBC's Brian Williams, in his first interview since being suspended in February, said "ego" drove him to embellish stories about his reporting experiences.
"I said things that weren't true," he told his colleague Matt Lauer in a taped interview on NBC's "Today" show.
Exaggerations -- like one that put him on a helicopter that was forced down by enemy fire in Iraq, when in fact he was on a different chopper -- "came from clearly a bad place, a bad urge inside me," he said. "This was clearly ego driven, the desire to better my role in a story I was already in."
But he said the moments were unintentional: "I wasn't trying to mislead people."
Williams delineated between his anchoring on "NBC Nightly News" -- where "I have always treated words very carefully" -- and his appearances on late night talk shows and other forums.
NBC said Thursday that most of the misstatements it found in an internal investigation were from those sorts of appearances.
"It had to have been ego that made me think I had to be sharper, funnier, quicker than anybody else," Williams told Lauer.
He also said "I own this" and repeatedly apologized.
Brian Williams interviewed by Matt Lauer.
With the interview, Williams essentially opened himself up to the court of public opinion, banking on the fact that he has been a popular news personality for decades.
Williams' suspension ends in August. He said the punishment period has been "torture," but "absolutely necessary."
NBC announced on Thursday afternoon that Williams would be staying in the corporate family in a reduced role, mainly by anchoring breaking news coverage and special reports on the cable news channel MSNBC.
Lester Holt will be the permanent anchor of "Nightly News," taking over after 10 years of Williams in the chair.
Williams confirmed to Lauer that he initially wanted his nightly anchor chair back and he "pushed back at first" when his bosses said no.
But he also said he was enthusiastic about the MSNBC job.
Asked to write the headline of his own story, Williams came up with: "A chastened and grateful man, mindful of his blessings, mindful of his mistakes, returns hoping for forgiveness and acceptance."
People have many more questions for Williams, about specific misstatements that were uncovered and what triggered them.
Williams indicated to Lauer that he doesn't want to address those specifics.
Given the opportunity to correct the record, Williams simply said, "I am sorry for what happened here. I am different as a result."
He said "there are going to be different rules of the road," but didn't say what they would be.
The next step in Williams' image rehabilitation comes on Friday evening when more of Lauer's interview airs on "Nightly News."
The comeback effort apparently also entails meetings with staffers.
It has been dubbed an "apology tour."
Williams spent time with "Nightly News" staffers on Thursday afternoon, shortly after the network made it official that he will not return to the newscast.
It was "incredibly emotional," and some people choked back tears, said an attendee, one of two people familiar with the meetings who described them on condition of anonymity.
Williams then traveled to Washington to meet with staffers at the NBC bureau there on Thursday evening.
Williams was "deeply apologetic" during his conversations with the Washington staffers, a source said.
The decision to bring Williams back, in a reduced role and reduced salary, capped months of deliberations by network executives.
"As you would imagine this was a difficult decision," Lack's boss, NBCUniversal CEO Steve Burke, said Thursday. "Brian Williams has been with NBC News for a very long time and he has covered countless news events with honor and skill. As I said in February, we believe in second chances, and I am hopeful that this new beginning will be good for Brian and the organization."
Burke optimistically added, "This matter has been extensively analyzed and deliberated on by NBC. We are moving forward."

My first chemotherapy session was excruciating. I got home and passed out and felt so awful and exhausted and nauseated and like it was the worst thing ever. I wondered what I had done to deserve it.
I had, thinking back on what really mattered, lived an exemplary life. I don’t just mean that I graduated from Harvard and Yale Law school with highest honours. That is not what matters. I mean I have not lost anyone along the way. No one ever gets over me. No one ever gives up on me. People disappear, sometimes even for years, but they always come back.
I’ve learned that when someone says “I hate your guts”, it’s just the beginning of the negotiation. They’ll be back. I’m impossible to let go. Do you hate charisma? Oh, who doesn’t. Everyone can’t stand it. You can’t bargain with it. It’s the bogeyman of personality. Well that’s me.
I apologise. I admit I was wrong. I take the blame. I say, I miss you. I say, I can’t live without you. I say, this isn’t right. I say, I love you. People love to hear what they love to hear. And I mean it. I know how to win people over. I know how to win readers over. I’m doing it right now. I know how to get people on my side from a distance, and that’s a pretty neat trick.
It is because I am honest. It is because I am not afraid. If it happens to anyone, it happens to me. I was given Viagra to counteract the sexual side effects of antidepressants. That happened. So it figures I would get breast cancer. It even makes sense I would get aggressive premenopausal breast cancer as a result of the BRCA2 mutation. It does not scare me. But the treatment is excruciating.
The night after my first chemotherapy session, I was swearing to my fiance that I would not go through it again. I was nauseated. I was exhausted like I’d just spent 40 years in the desert making the exodus from Egypt to Canaan. I did not care if cancer killed me, just not another night like this. But then the next morning, I felt OK. And I don’t want to die. I have too much left to do. All my mistakes are on the way to getting it right. All my failures are en route to success. I never lost a game; I only ran out of time. I can’t run out of time.
I don’t want cancer to change my life. People say it does. I guess it must. Everything does. We are affected by it all. This happens, that happens, we change. A delay on the subway, someone crashes their shopping trolley into us and it feels like an assault, all these little unimportant things change us. So I guess cancer has got to get to me. It is getting to me, of course. It’s going to mess up my hair. It makes me tired, and worse, it makes me cranky.
I accept that cancer is affecting me. But I don’t want it to change my life. I don’t want it to make me a better, worse, or even just a different person. I don’t want to give an illness that power. I spent much of my life battling who I am. I am now at peace. I’m good. I don’t need a new version. I am not obsolete. Cancer would win – not if it killed me, but if it changed me. It is a problem to be solved. It is not a revelation from on high.
But it already has surprised me. I did not know I was this tough. I did not know I could take this much pain without crying or complaining. I did not know I had this kind of composure. I appreciate the peace in the doctors I work with, how they worry about life and death, not Kim and Kanye. I appreciate how this removes me from normal concerns, at least somewhat. I still got married during the chemotherapy. I am still knitting one of my dearest friends a scarf. I still went to New Haven to talk to a class at Yale that read Prozac Nation, as I do every year, and had dinner with students, even though it was a long day. I am still mourning my dog Augusta constantly, because I lost her and I lost a piece of me I will never get back, and that does make me cry, that makes me wail. I am still writing, and thinking about law, and going out to dinner. I am still me.

This product contains all of the digits from 1 to 8. Can you complete it?
Answer: 64 * 58 = 3712.

Hence, 20% of 700 m is 140 m.
What per cent of Rs 4500 is Rs 9000?
Note: The sign of percentage (%) is removed dividing the number by 100.
In questions 24 to 59, fill in the blanks to make the statements true.
A_____with its denominator 100 is called a per cent.
A fraction with its denominator 100 is called a per cent.
15 kg is____% of 50 kg.
So, the number of students present on that day, was 46.
In a class of 50 students 8% were absent on one day. The number of students present on that day, was______.
So, the number of students present on that day, was 46.
Savitri obtained 440 marks out of 500 in an examination. She secured _____% marks in the examination.
Hence, Savitri secured 88% marks in the examination.
Out of a total deposit of Rs 1500 in her bank account, Abida withdrew 40% of the deposit. Now, the balance in her account is_____.
____ is 50% more than 60.
Let number be x. It is given that x is 50% more than 60.
John sells a bat for Rs 75 and suffers a loss of Rs 8. The cost price of the bat is___.
Hence, cost price of the bat is Rs 83.
If the price of sugar is decreased by 20%, then the new price of 3kg sugar originally costing Rs 120, will be______.
Given that, price of sugar is decreased by 20%.
Mohini bought a cow for Rs 9000 and Sold it at a loss of Rs 900. The selling price of the cow is_______.
Hence, the selling price of the cow is Rs 8100.
Devangi buys a chair for Rs 700 and sells it for Rs 750. She earns a profit of______% in the transaction.
Sonal bought a bed sheet for Rs 400 and sold it for Rs 440. Her____ % is___%.
Aahuti purchased a house for Rs 5059700 and spent Rs 40300 on its repairing. To make a profit of 5%, she should sell the house for Rs_______ .
If 20 lemons are bought for Rs 10 and sold at 5 for three rupees, then______in the transaction is_____%.
Narain bought 120 oranges at Rs 4 each. He sold 60% of the oranges at Rs 5 each and the remaining at Rs 3.50 each. His_____is_____%.
A fruit seller purchased 20 kg of apples at Rs 50 per kg. Out of these, 5% of the apples were found to be rotten. If he sells the remaining apples at Rs 60 per kg, then his_____is_____% .
Interest on Rs 3000 at 10% per annum for a period of 3 yr is______ .
Amount obtained by depositing Rs 20000 at 8% per annum for six months, is_____.
Interest on Rs 12500 at 18% per annum for a period of 2 yr and 4 months is______.
25 mL is_____% of 5 L.
If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then,_____% of A is equal to C.
Interest = , where T is_____,R% is____ and P is____.
Here, T is time period, R% is rate of interest and P is Principal.
The difference of interests for 2 yr and 3 yr on a sum of Rs 2100 at 8% per annum is_______.
To convert a fraction into a per cent, we______ it by 100.
To convert a fraction into a per cent, we multiply it by 100.
To convert a decimal into a per cent, we shift the decimal point two places to the_____.
To convert a decimal into a per cent, we shift the decimal point into places to the right.
The_____of interests on a sum of Rs 2000 at the rate of 6% per annum for yr and 2 yr is Rs 420.
When converted into percentage, the value of 6.5 is______than 100%.
Hence, when converted into percentage, the value of 6.5 is more than 100%.
In questions 68 and 59, copy each number line. Fill in the blanks, so that each mark on the number line is labelled with a per cent, a fraction and a decimal. Write all fractions in lowest terms.
In questions 60 to 79, state whether the statements are True or False.
When an improper fraction is converted into percentage, then the answer can also be less than 100.
Hence, when an improper fraction is converted into percentage, then the answer is always greater than 100.
8 h is 50% of 4 days.
Let 8 h be x% of 4 days.
The interest on Rs 350 at 5% per annum for 73 days is Rs 35.
12% of 120 is 100.
If Ankita obtains 336 marks out of 600, then percentage of marks obtained by her is 33.6%.
Hence, Ankita got 56% marks.
0.018 is equivalent to 8%.
50% of Rs 50 is Rs 25.
Hence, 50% of Rs 50 is Rs 25.
250 cm is 4% of 1 km.
Out of 600 students of a school, 126 go for a picnic. The percentage of students that did not go for the picnic, is 75.
Hence, 79% of students did not go for picnic.
By selling a book for Rs 50, a shopkeeper suffers a loss of 10%. The cost price of the book is Rs 60.
If a chair is bought for Rs 2000 and is sold at a gain of 10%, then selling price of the chair is Rs 2010.
If a bicycle was bought for Rs 650 and sold for Rs 585, then the percentage of profit is 10%.
Sushma sold her watch for Rs 3320 at a gain of Rs 320. For earning a gain of 10%, she should have sold the watch for Rs 3300.
Interest on Rs 1200 for yr at the rate of 15% per annum is Rs 180.
Amount received after depositing Rs 800 a period of 3 yr at the rate of 12% per annum is Rs 896.
Rs 6400 were lent to Feroz and Rashmi at 15% per annum for 3 and 5 yr, respectively. The difference in the interests paid by them is Rs 150.
A vendor purchased 720 lemons at Rs 120 per hundred. 10% of the lemons were found rotten, which he sold at Rs 50 per hundred. If he sells the remaining lemons at Rs 125 per hundred, then his profit will be 16%.
(a) 8% of Rs x is ? 100.
(b) 32% of x kg is 400 kg.
(c) 35% of Rs x is ?280.
(d) 45% of marks x is 405.
Imagine that, a 10 x 10 grid has value 300 and that this value is divided evenly among the small squares. In other words, each small square is worth 3. Use a new grid for each part of this problem and label each grid “Value : 300”.
(a) Shade 25% of the grid. What is 25% of 300? Compare the two answers.
(b) What is the value of 25 squares?
(c) Shade 17% of the grid. What is 17% of 300? Compare the two answers.
(d) What is the value of 1/10 of the grid?
Express as a per cent.
Express as a per cent.
Express as a per cent.
Express 80% as a fraction in its lowest form.
Express 33 % as a ratio in the lowest form.
Express 16 % as a ratio in the lowest form.
Express 150% as a ratio in the lowest form.
Sachin and Sanjana are calculating 23% of 800.
Now, calculate 52% of 700 using both the ways described above. Which way do you find easier?
Write 0.089 as a per cent.
Write 1.56 as a per cent.
What is 15% of 20?
What is 800% of 800?
What is 100% of 500?
What per cent of 1 h is 30 min?
What per cent of 1 day is 1 min?
What per cent of 1 km is 1000 m?
Find out 8% of 25 kg.
What per cent of Rs 80 is Rs 100?
45% of the population of a town are men and 40% are women. What is the percentage of children?
Hence, 15% of the population of a town are children.
The strength of a school is 2000. If 40% of the students are girls, then how many boys are there in the school?
Hence, number of boys in school is 1200.
Chalk contains 10% calcium, 3% carbon and 12% oxygen. Find the amount of carbon and calcium (in grams) in kg of chalk.
800 kg of mortar consists of 55% sand, 33% cement and rest lime. What is the mass of lime in mortar?
Hence, weight of lime in mortar is 96 kg.
In a furniture shop, 24 tables were bought at the rate of Rs 450 per table. The shopkeeper sold 16 of them at the rate of Rs 600 per table and the remaining at the rate of 400 per table. Find her gain or loss per cent.
Medha deposited 20% of her money in a bank. After spending 20% of the remainder, she has Rs 4800 left with her. How much did she originally have?
The cost of a flower vase got increased by 12%. If the current cost is Rs 896, what was its original cost?
Radhika borrowed Rs 12000 from her friends. Out of which Rs 4000 were borrowed at 18% and the remaining at 15% rate of interest per annum. What is the total interest after 3 yr?
A man travelled 60 km by car and 240 km by train. Find what per cent of total journey did he travel by car and what per cent by train?
By selling a chair for Rs 1440, a shopkeeper loses 10%. At what price, did he buy it?
Dhruvika invested money for a period from May 2006 to April 2008 at the rate of 12% per annum. If interest received by her is Rs 1620, then find the money invested.
A person wanted to sell a scooter at a loss of 25%. But at the last moment, he changed his mind and sold the scooter at a loss of 20%. If the difference in the two SP’s is Rs 4000, then find the CP of the scooter.
The population of a village is 8000. Out of these, 80% are literate and of these literate people, 40% are women. Find the ratio of the number of literate women to the total population.
In an entertainment programme, 250 tickets of Rs 400 and 500 tickets of Rs 100 were sold. If the entertainment tax is 40% on ticket of Rs 400 and 20% on ticket of Rs 100, then find how much entertainment tax was collected from the programme?
It is also given that, 40% and 20% of entertainment tax is on Rs 400 and Rs 100 tickets, respectively.
Bhavya earns Rs 50000 per month and spends 80% of it. Due to pay revision, her monthly income increases by 20% but due to price rise, she lias to spent 20% more. Find her new savings.
In an examination, there are three papers each of 100 marks. A candidate obtained 53 marks in the first paper and 75 marks in the second paper. How many marks must the candidate obtain in the third paper to get an overall of 70% marks?
A doctor reports blood pressure in millimetres of mercury (mm Hg) as a ratio of systolic blood pressure to diastolic blood pressure (such as 140 over 80). Systolic pressure is measured when the heart beats and diastolic pressure is measured when it rests. Refer to the table of blood pressure ranges for adults.
Manohar is a healthy 37 yr old man whose blood pressure is in the normal category.
(a) Calculate an approximate ratio of systolic to diastolic blood pressures in the normal range.
(b) If Manohar’s systolic blood pressure is 102 mm Hg, then use the ratio from part (a) to predict his diastolic blood pressure.
(c) Calculate ratio of average systolic to average diastolic blood pressures in the prehypertension category.
The king cobra can reach a Length of 558 cm. This is only about 60% of the length of the largest reticulated python. Find the length of the largest reticulated python.
Unequal masses will not balance on a fulcrum, if they are at equal distance from it, one side will go up and the other side will go down.
Unequal masses will balance when the following proportion is true.
The child on the left and child on the right are balanced. What is the mass of the child on the right?
A DNA model was built using the scale 2 cm : 0.0000001 mm. If the model of the DNA chain is 17 cm long, what is the length of the actual chain?
Given below are few mathematical terms.
(a) The ratio of consonants to vowels in each of the terms.
(b) The percentage of consonants in each of the terms.
What’s the Error? An analysis showed that 0.06% of the T-shirts made by one company were defective. A student says this is 6 out of every 100. What is the student’s error?
What’s the Error? A student said that the ratios and were proportional. What error did the student make?
Hence, the ratios are not proportional. To make a ratio proportional to another ratio, we just simply multiply both numerator and denominator by same number.
In our given case, student had multiply numerator by 3 and denominator by 4, which is incorrect.
What’s the Error? A clothing store charges Rs 1024 for 4 T-shirts. A student says that the unit price is Rs 25.6 per T-shirt. What is the error? What is the correct unit price?
A tea merchant blends two varieties of tea in the ratio of 5:4. The cost of first variety is Rs 200 per kg and that of second variety is Rs 300 per kg. If he sells the blended tea at the rate of Rs 275 per kg, then find out the percentage of his profit or loss.
Let green tea be 5x kg and lemon tea be 4x kg.
A piece of cloth 5 m long shrinks 10% on washing. How long will the cloth be after washing?
Nancy obtained 426 marks out of 600 and the marks obtained by Rohit are 560 out of 800. Whose performance is better?
A memorial trust donates Rs 500000 to a school, the interest on which is to be used for awarding 3 scholarships to students obtaining first three positions in the school examination every year. If the donation earns an interest of 12% per annum and the values of the second and third scholarships are Rs 20000 and Rs 15000 respectively, then find out the value of the first scholarship.
Ambika got 99% marks in Mathematics, 76% marks in Hindi, 61% in English, 84% in Science and 95% in Social Science. If each subject carries 100 marks, then find the percentage of marks obtained by Ambika in the aggregate of all the subjects.
What sum of money lent out at 16% per annum simple interest, so that it would produce Rs 9600 as interest in 2 yr?
Harish bought a gas-chullah for Rs 900 and later sold it to Archana at a profit of 5%. Archana used it for a period of two years and later sold it to Babita at a loss of 20%. For how much did Babita get it?
It is given that, Harish bought the chullah for Rs 900 and sold it to Archana at a profit of 5%.
In a debate competition, the judges decide that 20% of the total marks would be given for accent and presentation. 60% of the rest are reserved for the subject matter and the rest are for rebuttal. If this means 8 marks for rebuttal, then find the total marks.
Divide Rs 10000 in two parts, so that the simple interest on the first part for 4 yr at 12% per annum may be equal to the simple interest on the second part for 4.5 yr at 16% per annum.
per annum may be equal to the SI on second part for 4.5 yr at 16%.
Rs 9000 becomes Rs 18000 at simple interest in 8 yr. Find the rate per cent per annum.
In how many years, will the simple interest on a certain sum be 4.05 times the principal at 13.5% per annum?
The simple interest on a certain sum for 8 yr at 12% per annum is Rs 3120 more than the simple interest on the same sum for 5 yr at 14% per annum. Find the sum.
The simple interest on a certain sum for 2.5 yr at 12% per annum is Rs 300 less than the simple interest on the same sum for 4.5 yr at 8% per annum. Find the sum.
When you design your healthy diet, you want to make sure that you meet the dietary requirements to help you grow into a healthy adult. As you plan your menu, follow the following guidelines.
Calculate your ideal weight as per your height from the table given at the end of this question.
An active child should eat around 55.11 calories for each kilogram desired weight.
55% of calories should come from carbohydrates. There are 4 calories in each gram of carbohydrates.
15% of your calories should come from proteins. There are 4 calories in each gram of proteins.
30% of your calories may come from fats. There are 9 calories in each gram of fats.
Following is an example to design your own healthy diet.
150 students are studying English, Maths or both. 62% of students study English and 68% are studying Maths. How many students are studying both?
The table lists the world’s 10 largest deserts.
(a) What are the mean, median and mode of the areas listed?
(b) How many times the size of the Gobi Desert is the Namib Desert?
(c) What percentage of the deserts listed are in Asia?
(d) What percentage of the total area of the deserts listed is in Asia?
Earth’s total land is about 148428950 km2. The land area of Asia is about 30% of this total. What is the approximate land area of Asia to the nearest square kilometre?
The pieces of Tangrams have been rearranged to make the given shape.
By observing the given shape, answer the following questions.
(a) What percentage of total has been coloured?
(b) Check that the sum of all the percentages calculated above should be 100.
(c) If we rearrange the same pieces to form some other shape, will the percentage of colours change?

But I'm curious, how do you calculate or approximate the complexity of your algorithms?
1 but as they say, don't overdo it, premature optimization is the root of all evil, and optimization without a justified cause should deserve that name as well.
I'll do my best to explain it here on simple terms, but be warned that this topic takes my students a couple of months to finally grasp. You can find more information on the Chapter 2 of the Data Structures and Algorithms in Java book.
There is no mechanical procedure that can be used to get the BigOh.
As a "cookbook", to obtain the BigOh from a piece of code you first need to realize that you are creating a math formula to count how many steps of computations get executed given an input of some size.
The purpose is simple: to compare algorithms from a theoretical point of view, without the need to execute the code. The lesser the number of steps, the faster the algorithm.
The parameter N takes the data.length value. Now we need the actual definition of the function f(). This is done from the source code, in which each interesting line is numbered from 1 to 4.
There are many ways to calculate the BigOh. From this point forward we are going to assume that every sentence that doesn't depend on the size of the input data takes a constant C number computational steps.
We are going to add the individual number of steps of the function, and neither the local variable declaration nor the return statement depends on the size of the data array.
There is no mechanical rule to count how many times the body of the for gets executed, you need to count it by looking at what does the code do. To simplify the calculations, we are ignoring the variable initialization, condition and increment parts of the for statement.
Take away all the constants C.
From f() get the polynomium in its standard form.
Divide the terms of the polynomium and sort them by the rate of growth.
Keep the one that grows bigger when N approaches infinity.
There are a few tricks to solve some tricky ones: use summations whenever you can.
The first thing you needed to be asked is the order of execution of foo(). While the usual is to be O(1), you need to ask your professors about it. O(1) means (almost, mostly) constant C, independent of the size N.
The for statement on the sentence number one is tricky. While the index ends at 2 * N, the increment is done by two. That means that the first for gets executed only N steps, and we need to divide the count by two.
The sentence number two is even trickier since it depends on the value of i. Take a look: the index i takes the values: 0, 2, 4, 6, 8, ..., 2 * N, and the second for get executed: N times the first one, N - 2 the second, N - 4 the third... up to the N / 2 stage, on which the second for never gets executed.
Again, we are counting the number of steps. And by definition, every summation should always start at one, and end at a number bigger-or-equal than one.
We have a problem here: when i takes the value N / 2 + 1 upwards, the inner Summation ends at a negative number! That's impossible and wrong. We need to split the summation in two, being the pivotal point the moment i takes N / 2 + 1.
Since the pivotal moment i > N / 2, the inner for won't get executed, and we are assuming a constant C execution complexity on its body.
Big O gives the upper bound for time complexity of an algorithm. It is usually used in conjunction with processing data sets (lists) but can be used elsewhere.
A few examples of how it's used in C code.
If we wanted to access the first element of the array this would be O(1) since it doesn't matter how big the array is, it always takes the same constant time to get the first item.
This would be O(n) since at most we would have to look through the entire list to find our number. The Big-O is still O(n) even though we might find our number the first try and run through the loop once because Big-O describes the upper bound for an algorithm (omega is for lower bound and theta is for tight bound).
This is O(n^2) since for each pass of the outer loop ( O(n) ) we have to go through the entire list again so the n's multiply leaving us with n squared.
This is barely scratching the surface but when you get to analyzing more complex algorithms complex math involving proofs comes into play. Hope this familiarizes you with the basics at least though.
While knowing how to figure out the Big O time for your particular problem is useful, knowing some general cases can go a long way in helping you make decisions in your algorithm.
Small reminder: the big O notation is used to denote asymptotic complexity (that is, when the size of the problem grows to infinity), and it hides a constant.
This means that between an algorithm in O(n) and one in O(n2), the fastest is not always the first one (though there always exists a value of n such that for problems of size >n, the first algorithm is the fastest).
Note that the hidden constant very much depends on the implementation!
Also, in some cases, the runtime is not a deterministic function of the size n of the input. Take sorting using quick sort for example: the time needed to sort an array of n elements is not a constant but depends on the starting configuration of the array.
A good introduction is An Introduction to the Analysis of Algorithms by R. Sedgewick and P. Flajolet.
As you say, premature optimisation is the root of all evil, and (if possible) profiling really should always be used when optimising code. It can even help you determine the complexity of your algorithms.
Seeing the answers here I think we can conclude that most of us do indeed approximate the order of the algorithm by looking at it and use common sense instead of calculating it with, for example, the master method as we were thought at university. With that said I must add that even the professor encouraged us (later on) to actually think about it instead of just calculating it.
which recursively calculates the factorial of the given number.
The first step is to try and determine the performance characteristic for the body of the function only in this case, nothing special is done in the body, just a multiplication (or the return of the value 1).
So the performance for the body is: O(1) (constant).
Next try and determine this for the number of recursive calls. In this case we have n-1 recursive calls.
So the performance for the recursive calls is: O(n-1) (order is n, as we throw away the insignificant parts).
Peter, to answer your raised issues; the method I describe here actually handles this quite well. But keep in mind that this is still an approximation and not a full mathematically correct answer. The method described here is also one of the methods we were taught at university, and if I remember correctly was used for far more advanced algorithms than the factorial I used in this example.
Of course it all depends on how well you can estimate the running time of the body of the function and the number of recursive calls, but that is just as true for the other methods.
I think about it in terms of information. Any problem consists of learning a certain number of bits.
Your basic tool is the concept of decision points and their entropy. The entropy of a decision point is the average information it will give you. For example, if a program contains a decision point with two branches, it's entropy is the sum of the probability of each branch times the log2 of the inverse probability of that branch. That's how much you learn by executing that decision.
For example, an if statement having two branches, both equally likely, has an entropy of 1/2 * log(2/1) + 1/2 * log(2/1) = 1/2 * 1 + 1/2 * 1 = 1. So its entropy is 1 bit.
Suppose you are searching a table of N items, like N=1024. That is a 10-bit problem because log(1024) = 10 bits. So if you can search it with IF statements that have equally likely outcomes, it should take 10 decisions.
That's what you get with binary search.
Suppose you are doing linear search. You look at the first element and ask if it's the one you want. The probabilities are 1/1024 that it is, and 1023/1024 that it isn't. The entropy of that decision is 1/1024*log(1024/1) + 1023/1024 * log(1024/1023) = 1/1024 * 10 + 1023/1024 * about 0 = about .01 bit. You've learned very little! The second decision isn't much better. That is why linear search is so slow. In fact it's exponential in the number of bits you need to learn.
Suppose you are doing indexing. Suppose the table is pre-sorted into a lot of bins, and you use some of all of the bits in the key to index directly to the table entry. If there are 1024 bins, the entropy is 1/1024 * log(1024) + 1/1024 * log(1024) + ... for all 1024 possible outcomes. This is 1/1024 * 10 times 1024 outcomes, or 10 bits of entropy for that one indexing operation. That is why indexing search is fast.
Now think about sorting. You have N items, and you have a list. For each item, you have to search for where the item goes in the list, and then add it to the list. So sorting takes roughly N times the number of steps of the underlying search.
So sorts based on binary decisions having roughly equally likely outcomes all take about O(N log N) steps. An O(N) sort algorithm is possible if it is based on indexing search.
I've found that nearly all algorithmic performance issues can be looked at in this way.
Arithmetic operations (e.g. + or %).
Structure accessing operations (e.g. array-indexing like A[i], or pointer fol- lowing with the -> operator).
Simple assignment such as copying a value into a variable.
Calls to library functions (e.g., scanf, printf).
Assignment statements that do not involve function calls in their expressions.
Write statements that do not require function calls to evaluate arguments.
The jump statements break, continue, goto, and return expression, where expression does not contain a function call.
uses index variable i. It increments i by 1 each time around the loop, and the iterations stop when i reaches n − 1.
However, for the moment, focus on the simple form of for-loop, where the difference between the final and initial values, divided by the amount by which the index variable is incremented tells us how many times we go around the loop. That count is exact, unless there are ways to exit the loop via a jump statement; it is an upper bound on the number of iterations in any case.
For instance, the for-loop iterates ((n − 1) − 0)/1 = n − 1 times, since 0 is the initial value of i, n − 1 is the highest value reached by i (i.e., when i reaches n−1, the loop stops and no iteration occurs with i = n−1), and 1 is added to i at each iteration of the loop.
In the simplest case, where the time spent in the loop body is the same for each iteration, we can multiply the big-oh upper bound for the body by the number of times around the loop. Strictly speaking, we must then add O(1) time to initialize the loop index and O(1) time for the first comparison of the loop index with the limit, because we test one more time than we go around the loop. However, unless it is possible to execute the loop zero times, the time to initialize the loop and test the limit once is a low-order term that can be dropped by the summation rule.
We know that line (1) takes O(1) time. Clearly, we go around the loop n times, as we can determine by subtracting the lower limit from the upper limit found on line (1) and then adding 1. Since the body, line (2), takes O(1) time, we can neglect the time to increment j and the time to compare j with n, both of which are also O(1). Thus, the running time of lines (1) and (2) is the product of n and O(1), which is O(n).
We have already established that the loop of lines (3) and (4) takes O(n) time. Thus, we can neglect the O(1) time to increment i and to test whether i < n in each iteration, concluding that each iteration of the outer loop takes O(n) time.
The initialization i = 0 of the outer loop and the (n + 1)st test of the condition i < n likewise take O(1) time and can be neglected. Finally, we observe that we go around the outer loop n times, taking O(n) time for each iteration, giving a total O(n^2) running time.
If you want to estimate the order of your code empirically rather than by analyzing the code, you could stick in a series of increasing values of n and time your code. Plot your timings on a log scale. If the code is O(x^n), the values should fall on a line of slope n.
This has several advantages over just studying the code. For one thing, you can see whether you're in the range where the run time approaches its asymptotic order. Also, you may find that some code that you thought was order O(x) is really order O(x^2), for example, because of time spent in library calls.
Basically the thing that crops up 90% of the time is just analyzing loops. Do you have single, double, triple nested loops? The you have O(n), O(n^2), O(n^3) running time.
Break down the algorithm into pieces you know the big O notation for, and combine through big O operators. That's the only way I know of.
For more information, check the Wikipedia page on the subject.
Big O notation is useful because it's easy to work with and hides unnecessary complications and details (for some definition of unnecessary). One nice way of working out the complexity of divide and conquer algorithms is the tree method. Let's say you have a version of quicksort with the median procedure, so you split the array into perfectly balanced subarrays every time.
Now build a tree corresponding to all the arrays you work with. At the root you have the original array, the root has two children which are the subarrays. Repeat this until you have single element arrays at the bottom.
Since we can find the median in O(n) time and split the array in two parts in O(n) time, the work done at each node is O(k) where k is the size of the array. Each level of the tree contains (at most) the entire array so the work per level is O(n) (the sizes of the subarrays add up to n, and since we have O(k) per level we can add this up). There are only log(n) levels in the tree since each time we halve the input.
Therefore we can upper bound the amount of work by O(n*log(n)).
and lets just assume the a and b are BigIntegers in Java or something that can handle arbitrarily large numbers. Most people would say this is an O(n) algorithm without flinching. The reasoning is that you have n iterations in the for loop and O(1) work in side the loop.
So this algorithm runs in quadradic time!
Familiarity with the algorithms/data structures I use and/or quick glance analysis of iteration nesting. The difficulty is when you call a library function, possibly multiple times - you can often be unsure of whether you are calling the function unnecessarily at times or what implementation they are using. Maybe library functions should have a complexity/efficiency measure, whether that be Big O or some other metric, that is available in documentation or even IntelliSense.
Less useful generally, I think, but for the sake of completeness there is also a Big Omega Ω, which defines a lower-bound on an algorithm's complexity, and a Big Theta Θ, which defines both an upper and lower bound.
As to "how do you calculate" Big O, this is part of Computational complexity theory. For some (many) special cases you may be able to come with some simple heuristics (like multiplying loop counts for nested loops), esp. when all you want is any upper bound estimation, and you do not mind if it is too pessimistic - which I guess is probably what your question is about.
If you really want to answer your question for any algorithm the best you can do is to apply the theory. Besides of simplistic "worst case" analysis I have found Amortized analysis very useful in practice.
For the 1st case, the inner loop is executed n-i times, so the total number of executions is the sum for i going from 0 to n-1 (because lower than, not lower than or equal) of the n-i. You get finally n*(n + 1) / 2, so O(n²/2) = O(n²).
For the 2nd loop, i is between 0 and n included for the outer loop; then the inner loop is executed when j is strictly greater than n, which is then impossible.
In addition to using the master method (or one of its specializations), I test my algorithms experimentally. This can't prove that any particular complexity class is achieved, but it can provide reassurance that the mathematical analysis is appropriate. To help with this reassurance, I use code coverage tools in conjunction with my experiments, to ensure that I'm exercising all the cases.
As a very simple example say you wanted to do a sanity check on the speed of the .NET framework's list sort. You could write something like the following, then analyze the results in Excel to make sure they did not exceed an n*log(n) curve.
In this example I measure the number of comparisons, but it's also prudent to examine the actual time required for each sample size. However then you must be even more careful that you are just measuring the algorithm and not including artifacts from your test infrastructure.
Don't forget to also allow for space complexities that can also be a cause for concern if one has limited memory resources. So for example you may hear someone wanting a constant space algorithm which is basically a way of saying that the amount of space taken by the algorithm doesn't depend on any factors inside the code.
Sometimes the complexity can come from how many times is something called, how often is a loop executed, how often is memory allocated, and so on is another part to answer this question.
Lastly, big O can be used for worst case, best case, and amortization cases where generally it is the worst case that is used for describing how bad an algorithm may be.
What often gets overlooked is the expected behavior of your algorithms. It doesn't change the Big-O of your algorithm, but it does relate to the statement "premature optimization. . .."
Expected behavior of your algorithm is -- very dumbed down -- how fast you can expect your algorithm to work on data you're most likely to see.
For instance, if you're searching for a value in a list, it's O(n), but if you know that most lists you see have your value up front, typical behavior of your algorithm is faster.
To really nail it down, you need to be able to describe the probability distribution of your "input space" (if you need to sort a list, how often is that list already going to be sorted? how often is it totally reversed? how often is it mostly sorted?) It's not always feasible that you know that, but sometimes you do.
Disclaimer: this answer contains false statements see the comments below.
If you're using the Big O, you're talking about the worse case (more on what that means later). Additionally, there is capital theta for average case and a big omega for best case.
f(n) = O(g(n)) means there are positive constants c and k, such that 0 ≤ f(n) ≤ cg(n) for all n ≥ k. The values of c and k must be fixed for the function f and must not depend on n.
Ok, so now what do we mean by "best-case" and "worst-case" complexities?
This is probably most clearly illustrated through examples. For example if we are using linear search to find a number in a sorted array then the worst case is when we decide to search for the last element of the array as this would take as many steps as there are items in the array. The best case would be when we search for the first element since we would be done after the first check.
The point of all these adjective-case complexities is that we're looking for a way to graph the amount of time a hypothetical program runs to completion in terms of the size of particular variables. However for many algorithms you can argue that there is not a single time for a particular size of input. Notice that this contradicts with the fundamental requirement of a function, any input should have no more than one output. So we come up with multiple functions to describe an algorithm's complexity. Now, even though searching an array of size n may take varying amounts of time depending on what you're looking for in the array and depending proportionally to n, we can create an informative description of the algorithm using best-case, average-case, and worst-case classes.
Sorry this is so poorly written and lacks much technical information. But hopefully it'll make time complexity classes easier to think about. Once you become comfortable with these it becomes a simple matter of parsing through your program and looking for things like for-loops that depend on array sizes and reasoning based on your data structures what kind of input would result in trivial cases and what input would result in worst-cases.
If we have a sum of terms, the term with the largest growth rate is kept, with other terms omitted.
If we have a product of several factors constant factors are omitted.
If we simplify f(x), where f(x) is the formula for number of operations done, (4n^2 + 2n + 1 explained above), we obtain the big-O value [O(n^2) in this case]. But this would have to account for Lagrange interpolation in the program, which may be hard to implement. And what if the real big-O value was O(2^n), and we might have something like O(x^n), so this algorithm probably wouldn't be programmable. But if someone proves me wrong, give me the code . . . .
For code A, the outer loop will execute for n+1 times, the '1' time means the process which checks the whether i still meets the requirement. And inner loop runs n times, n-2 times.... Thus,0+2+..+(n-2)+n= (0+n)(n+1)/2= O(n²).
I would like to explain the Big-O in a little bit different aspect.
Big-O is just to compare the complexity of the programs which means how fast are they growing when the inputs are increasing and not the exact time which is spend to do the action.
IMHO in the big-O formulas you better not to use more complex equations (you might just stick to the ones in the following graph.) However you still might use other more precise formula (like 3^n, n^3, ...) but more than that can be sometimes misleading! So better to keep it as simple as possible.
I would like to emphasize once again that here we don't want to get an exact formula for our algorithm. We only want to show how it grows when the inputs are growing and compare with the other algorithms in that sense. Otherwise you would better use different methods like bench-marking.
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b. What proportion of the population is between 12.2 and 14.3?
c. What proportion of the population is less than 10.0?

IFComp is closed to votes. The games are still playable on the site and will remain so, and the results will be announced at 4pm EST (2100 GMT) tomorrow.
It has been so much fun to participate in IFComp again. Everybody’s game made some people smile, and I hope and trust that most authors entered to share their creativity and take part in an important IF community event, rather than out of wanting to beat other people. Prefacing cliches with “It’s a cliche but” is a cliche, but it’s a cliche but we all win.
These are my brief impressions of other people’s IFComp games. REVIEWING IS HARD: I don’t have full reviews, I haven’t played as many games as I’d like, I haven’t written up every game I played or liked, and I haven’t said as much as I’d like to about most of the games I did write up.
Spoilers are rot13‘d and coloured pink.
I’d assumed at first that my goal was to escape from the motel, so it was a little jarring when I realised I was supposed to want to stay, or at least the protagonist wanted to. Then shortly after I’d shrugged and decided to play as if I want to stay, she decided she wanted to leave.
I didn’t get the chance to Have A Talk with Lex before I got to my ending, but I assume that possibility is in there somewhere. I certainly enjoyed myself enough to try for another ending once I’ve had a chance to forget some things.
This is funny, and busy, and highly replayable. All of the NPCs are entertaining and the small scope and timespan really work to its advantage.
First impressions, the graphics in the web version are beautiful, and it’s an innovative idea.
I’m still getting used to the game itself – like many players, I didn’t quite clock the existence of the rulebook until I’d been playing a while – but it certainly makes me want to learn the tactics.
There’s something really nice about the layers of abstraction and stories-within-stories here – it’s an IF game, about going to a tournament, to play a card game, that itself tells a story about war.
I’d pay money for a printed Game of Worlds set.
My favourite so far. It’s an unashamed puzzle with a reduced parser – the only commands it accepts are NORTH, EAST, SOUTH, WEST, WAIT, LOOK and STATUS, with actions like picking things up and giving them to NPCs triggered automatically. This is surprisingly effective, and the game contains a variety of puzzles of different types. There was one that I solved by accident (tvivat gur ynopbng gb gur znvyebbz pyrex) and a couple where I resorted to the walkthrough (Tebire gur tneqrare, naq gur purzvpny zvkvat ng gur raq) but neither of those felt unfair in retrospect.
I was initially put off by the request to print off a map to fill in as you go, but found it added to the fun, like solving a crossword, and there are certainly puzzles that would have been both harder and less enjoyable without it.
The author knows how to use brevity of writing to good effect – with such a large map, longer descriptions would have made the game more tiring. But they managed to squeeze every drop of clarity and characterisation out of the one-sentence descriptions: I even ungrq Gunqqrhf, naq jnf qryvtugrq gb frr uvz fghoovat uvf gbr nsgre tvivat uvz gur zvfsbeghangbe.
Loved this one. It’s another game with an extremely reduced verbset – reduced to zero – but it has a HUGE number of nouns. I think I got a default response maybe twice, and it’s well enough handled that I’m not even certain they were default responses. This is the way to do a puzzleless game without sacrificing the player’s sense of agency. The excellent, slightly disconcerting prose and the horror-adjacent theme were all very Chandler Groover. Anyone who’s a fan of his other works will enjoy this, and probably has already.
Somehow, this is the first time I’ve played a Quest game, and I have to begin by saying how impressed I am with the Quest platform. It’s smooth, lets you click links or type into a parser, and I found it more comfortable to use than any of the web-based Inform/TADS interpreters. I later found out that it has a tendency for it to time out, though, which is a dealbreaker.
As to the game itself: this is a horror story with a child protagonist set in the ’80s or ’90s, so it immediately put me in mind of “Stranger Things”. The atmosphere is created skilfully, making the right nostalgic feeling from the childish perspective and the presence of Ataris, trapperkeepers and so on. For me, the puzzle involving gnxvat onggrevrf sebz lbhe cneragf’ frk gbl broke it a bit – apart from general squeamishness, it relied on me having knowledge that the player character didn’t.
It suffers a lot from underimplementation: many items mentioned in the room descriptions give an “I can’t see that” response. Worse, many objects are referred to by nouns *in their description* that aren’t supported by the parser, such as the “Betamax cassette” which you have to refer to as TAPE. Reasonable verbs are also unsupported – PULL CURTAIN works but OPEN CURTAIN doesn’t. The description of the flashlight says it doesn’t work, even after you put the batteries in it.
After I explored most of the house, it abruptly stopped responding to commands and I gave up. I’ll have another go later, when the author has hopefully had time to fix some bugs.
This is a fairly linear Twine story about a bear infiltrating a secret arms facility for… some reason. There are flashbacks to the bear’s childhood and abusive father, which I found tough going, and flash-sidewayses to a simultaneous scene involving some of the people working in the facility. I would have liked to know more about the bear himself and exactly what he’s doing there.
It’s great to see so many of the games experimenting with interfaces and world models in this comp. This one is an implementation of a CRPG, with stats, levels and combat, using a text interface written in Ruby, with input by way of one- or two-key choices. It felt like something between a roguelike and a parser game. I was compelled by the story, even though it’s little more than an old-fashioned forest-and-cave crawl, but found the interface a bit repetitive and clunky, especially in combat, where the well-written descriptions are undermined by the fact that after a short time you’re just scanning for the numbers. The author has hinted that they’re going to redo this as a browser game with link-driven controls and separate windows, and I look forward to playing that incarnation.
That’s worth at least a 2 in my book.
Spring Thing has been brilliant. I’m grateful to all the organisers, authors and players.
My game The Xylophoniad won the Alumni’s Choice ribbon, by which I’m delighted and, frankly, floored. Astrid Dalmady’s Tangaroa Deep won Audience Choice.
I haven’t played all the games yet, and as a participant I was never planning to write full reviews. Here are my thoughts on some of the games I’ve got round to, in no order at all.
Brilliantly macabre. The PC is a stage conjurer in what feels like a sort of grotesque Victorian circus setting, trying to outdo their smarmy rival. The playing area is small, but intricately implemented, and uses an ingenious navigation system (the only directions that matter are IN and OUT) to give a sense of being much larger. The twist, when it comes, is both horrifying and hilarious. Of all the games I played, this is the one I would have put money on getting a ribbon.
This is one of those games where I am not sure what was going on, but I’m sure I enjoyed it. Dr Sourpuss is a talking, mortar-board wearing cat created by a genetic-engineering accident involving a lemon tree. He and a couple of other characters take the player on a winding story involving a sinister corporation that manufactures multiple-choice test marking machines, making good use of absurdity to smuggle a clever commentary on the effect of standardised, one-size-fits-all education on students. The puzzles are simple but clever: some objects, when they are mentioned in the story, appear in your inventory, and at any time you can go to a lab and choose two of them to combine into some new object that is the key to getting past each stage.
Deep-sea diving simulation with excellent atmospheric writing, and a deserving winner of the Audience Choice ribbon. Like Will Crowther’s orginal Adventure before the fantasy elements were added, it’s an effective simulation in words of exploring a space, with some ambiguous fantasy elements in some endings. The conversation between the PC and her assistant on the surface is charming, and in a nice touch, the ending shows you pictures of the sea creatures you encountered.
A surreal horror story. The text appears in a typewriting effect, which I thought was unnecessary till I saw someone else point out that this is a clever way of making players read rather than skim. Unfortunately I accidentally closed my browser somewhere near the end of the game, and the unskippable slow text made it too much trouble to catch up again (I’ll replay when I’ve had some time to forget the story so I can enjoy it again from the start.) The sound, illustrations and design were excellent.
A “cartoon animal noir” game in the vein of Who Framed Roger Rabbit or Jasper Fforde’s Nursery Crime books. I’m not familiar enough with the Veeder canon to get all the in-jokes, but enough to see why it won first place in Ryan’s Exposition. It stands on its own as a comic story anyway. As someone on &if said, noir is already abstracted enough from reality that making the characters cartoon animals actually adds something to the style.

Tom Lopez teaches at the Oberlin College Conservatory of Music; Assistant Professor of Computer Music and Digital Arts. He is also the Director of the Computer Music Program at The Walden School.
Tom has received awards from the National Endowment for the Arts, the Aaron Copland Fund, the Mid-America Arts Alliance, the Knight Foundation, the Disney Foundation, Meet the Composer, ASCAP, and a Fulbright Fellowship as composer-in-residence at the Centre International de Recherche Musical in Nice, France. He has appeared at festivals and conferences around the world as a guest lecturer and composer. Tom has served on the executive committee of SCI (Society of Composers, Inc.) and was president of the Texas Computer Musicians Network. He has been a resident artist at the Atlantic Center for the Arts, the Copland House, Villa Montalvo, and Djerassi. His compositions have received critical acclaim and peer recognition; including a Grant for Young Composers by ASCAP for Vocal Sketch #2, and releases on CD by SEAMUS (Society for Electro-Acoustic Music in the United States) for Curvatures and by SEAMUS and SCI for Hollow Ground II. His music has been performed around the world and throughout the United States including The Kennedy Center.
"The most artistically satisfying work on the program was Tom Lopez's 'They Hearken to Echoes,' an incredibly effective, lightly staged work for two flutists that draws its inspiration from architect Louis Sullivan, whose objects appear to transform objects at a distance to a point of closeness.
Using great imagination and a keen sense for the dramatic, Lopez invokes a slow but relentless sequence of canonic, imitative and echo-driven effects that achieves the coming together of the two flutists from afar-musically and spatially. The performers begin at opposite ends of the hall and gradually approach each other, as the echoes eventually turn into a two-part invention until the flutes ultimately meld into a unison synchronization of pitch and timbre. Flutists Kelly Covert and Kristin Bacchiocchi achieved an impressive, symbiotic blend of tone and color."
They Hearken to Echoes was composed in Austin, Texas (1997, revised in Oberlin, Ohio 2001). The title, which describes the performers both literally and metaphorically, is from the writings of architect Louis Sullivan. The overall design of the piece moves from distance to closeness; with respect to the physical placement of performers, with respect to melodic, harmonic, and rhythmic material, and especially with respect to echoes. Perhaps it is a "call-response" work, where the response time gradually diminishes until the call and the response are simultaneous. Or perhaps it is a canon modeled on a drawing by M.C. Escher, in which the second voice slowly gains ground until both voices share a moment of synchronicity.
Curvatures was composed in Oberlin, Ohio (2001, revised in Oberlin, 2004). This work was created for amplified string quartet (acoustic or Zeta instruments) and live electronics. The sounds of the quartet are manipulated with effects units or a computer. Signal processing techniques modify the timbral characteristics of the quartet; sometimes to a large degree but very often in subtle ways, allowing the audience to wonder whether particular sounds are from the real quartet or a virtual quartet. One of my compositional goals was to traverse a wide range of sonic worlds. Within a relatively short piece, the music navigates between fast and slow, thick and thin, chaotic and serene, minimal and fugal, cerebral and emotional, and so on. I wanted to compose a piece that would keep the listener on their toes, present occasional surprises, and provide something for the body and the brain.
Hollow Ground II was composed in Austin, Texas (1996). Written for soprano voice and prerecorded sound, this work has been performed with dance choreographed by Yacov Sharir. As it is the second piece in a trilogy commissioned by the Sharir Dance Company, it contains some of the sonic material from its predecessor Hollow Ground I; no other pre-existing musical sources were incorporated. Both works contain various acoustic instruments lying around my apartment at the time; shakers, rattles, rain sticks, finger cymbals, computers, and so on. Despite the addition of a vocalist, Hollow Ground II does not have any text; the vocalist never sings a word-her sounds are syllabic, which, when combined with her physical gestures during performance, create a strong ritualistic quality. Perhaps this is a kind of indigenous music; that is, music generated from making the most out of the materials within arm's reach. With an internal drive to create, an artist will use whatever is available to achieve their expression; the "whatever" one uses is local, but the desire to "express" is global.
Lorelei was composed in Austin, Texas (1995). The title refers to a siren, in Germanic legends, whose beautiful singing lured sailors to shipwreck. Such evocative singing is also attributed with guiding recently-departed souls to heaven. The work is in three movements. The first movement is "Pure," English for the German word, "rein." The second movement is "Heart," English for the German word, "hard." The third movement is, "Reins," an English word defining the part of the body which is the source of affection and passion. Lorie Lee Reinhard (April 1, 1970 - June 29, 1987) died in a car accident on the roads of rural Ohio. The driver also died and two additional passengers were injured.

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The International Astronomical Union (IAU) recently signed an agreement to establish an Office of Astronomy Development (OAD) in South Africa to focus the agency's mission to foster astronomy worldwide.
"It?s a really big push for the astronomy development globally, to have this office," said IAU Press Officer Lars Lindberg Christensen. "It's really a fairly big thing. It's going to be well-staffed, and well-funded. It will really move to help astronomy proliferate in parts of the world where it's really not so predominant."
Housed at the South African Astronomical Observatory in Tshwane/Pretoria, the office will be a first for the IAU. Until now, the organization, which boasts 10,000 individual members from 90 countries, has conducted its activities through a network with no central location.
So far, the office has been set up for a period of five years, Lindberg Christensen said. Hoping to extend that to a total of 10 years, the IAU plans to use the time to advance a central goal: increasing the degree to which less-developed countries participate in astronomy and fundamental science.
Current ideas on the table involve using the network of those working in astronomy and education to build resource-rich nodes in disadvantaged regions. Major components of the plan include teacher training, scientist-taught regional schools for young people, and institute twinning, where organizations in the developed world will team up with those in less-developed countries. Even brief visits and lectures by educators or prominent astronomers to certain areas of the world can stimulate interest in the topic, itself an achievement and critical step towards building a strong foundation, Lindberg Christensen said.
"In a sense astronomy is in a sweet spot compared to other sciences," Lindberg Christensen told SPACE.com. "It has unique cultural and technological aspects that make it easier to use it as a wave breaker for the fundamental sciences in general."
"Some of the other types of hot sciences have a really hard time for students to visualize the importance of what they're doing," he added. "Astronomy is so inspiring, it's so visual; it deals with questions that are important to mankind: Are we unique? Are there other planets that have life on them? And that makes it easier to open people's eyes, and that makes it easier to open them to research."
Though the UN Millennium Goals, a set of goals agreed upon by UN member states to improve the wellbeing of humans worldwide, include aims for the development of primary education and widespread networks, attention for these needs easily shifts in the face of immediate concerns like hunger and health, Lindberg Christensen said.
"Society in general is focusing more on short-term benefits. But astronomy and physics is not belonging to that category. The returns come in 50 or maybe 100 years. And this is why it is so important to open eyes to the importance of these sciences," Lindberg Christensen said.
retary of the IAU, Ian Corbett, formalizes a decision taken in May 2010 when the IAU selected South Africa as the host for the OAD. The South African bid beat stiff competition from a field of 20 competing proposals.
According to Lindberg Christensen, South Africa was selected because of its rich tradition in astronomy, and the unique balances offered by its location in the world. As an area very important in terms of development, Sub-Saharan Africa is also not completely undeveloped, he said.
"This is a momentous occasion and the start of something really new, which should have profound, far-reaching long-term consequences for us all and not just for the developing countries," said IAU General Secretary Corbett. "It is wonderful that South Africa has joined with the IAU in this endeavor, and has demonstrated the determination and commitment necessary to make this a success."

Summer is already a while to end and also the autumn is no longer long. It is all the more important that we to follow soon. For the cold winter months are approaching and then it is time to buy the matching shoes, to be prepared against the cool weather conditions. However, the fashionable aspect should by no means short come. The matching shoes complete the outfit really and seem fashionable and contemporary woman. While in winter 2012 especially patent leather, suede leather, metallic and shiny materials bribed and, frequently seen cinnamon and Curry on the streets were just warm Browns such as cognac, other trends prevail this year, where it is worth a closer look. As in the past years a variety is offered us of ways to express your own personality through various design elements as well as to rediscover familiar in the shops. The creative aspect of increasing this year with rivets, stones and Buckles, while the long proven vintage look moves more and more into the background. In addition, shoes made of leather can be observed again increasingly. Also in the colors and the amount of paragraphs a lot is make sure to leave the front door not completely out of fashion.
The color of shoes, some colors are to name a few, that never go out of fashion over the years. So, for example black shoes always fit and never wrong Act. Also pumps, who received a small variation in the form of condensed spikes last year, are still acceptable this year. Who however necessarily his individuality would like to live out, may do so again this year. Whether colorful or single color, who feel comfortable in his shoes, is maybe not always the trend, can handle however carefree everyday life.
Straight lace shoes, such as special ballerinas and loafers, are again in demand and thus remain in the trend. Finally they complement each other perfectly to a variety of outfits, or on a visit to friends and acquaintances in the Office.
Besides ballerinas and loafers are also boots and ankle boots still not out of fashion. However, this competition will receive from the riding-boots. Because fashion is currently total somewhat simple, the boots very well for an appropriate outfit in this suitable season. They are therefore particularly like to elected to classic and stylish outfits, so these shoes give an elegant and timeless impression.
The famous UGG boots are especially recommended for very cold days. Although not exceptionally new, however they provide warm protection, high, lined or unlined. Fashionably seen we do anything wrong so this year, were impossible to imagine these shoes in the past years.
As mentioned above, black is also in this year for many outfits and continue to lose not his role under the colors of shoes. This winter, it is particularly striking that this color is dominant.
A shoe in black or black boots have very elegant while rivets and buckles give the shoes in addition a slightly rockier feel and more individuality. Although black is the most represented color, however appropriate specimens can be with the various designs such as the aforementioned buckles and studs for every taste and for every outfit in winter 2013 found.
Who wants to wear not only black shoes, can be reassured. To an outfit, consisting of dark shades, which offers distractions coming winter with gemstone colors such as Emerald and Ruby Red refreshing and it allows women, is also something to highlight here.
Camouflage prints are this year in the agreement on the feet. The appealing “stealth look” fits many fashionable outfits and so flexible. Also, one way is to wear a modified variation of this pattern, which, for example, slightly dissolute looks. Then, the Viewer on the road or in the Office only at the second glance recognizes that it is the camouflage pattern.
Who however don’t like this trend, which can stand out with the animal prints. This prints “running” always fashionably seen nothing is wrong there?
The materials continues the trend from last year. The used look or even the vintage effects lose more and more in importance. This year, however, the factor of “Shine” is prominent. This unfolds over leather or metallic effects. Smooth and Matt leather combinations are this year particularly in fashion, so that special effects and more variation is awarded an outfit.
The paragraphs is to determine, however, that the trend has become lower heels. These are clearly flat this year. We have nothing to fear but to the beloved high-heeled shoes, because they are always fashionable and look still tempting. Who would like to have but not too flat or too high, the block or Queenie paragraphs to provide the appropriate compromise. Be adjusted should the so-called wedges but with wedge heels. Have lost significantly in beam power since last winter.
The motto is: “the jewelry, the better”. Now, everything that decorates the shoes and matching decorated is well suited. Rivets and small metal spots on the shoes are impossible to imagine and accentuate the style of punk-chic ideal. Many shoes are now also increasingly finding buckles, as in riding boots, boots Enrique and co. The shoes appear more noble and classic.
When all decorations should be that they not achieve layered effect despite everything and be through exaggerations to “bunt” sure however. Showy decorated shoes do not work and cast a bad light on the carrier and the entire outfit.
This year, the fashion world of shoes is undergoing a transformation and continuous development. Some models, such as shoes with a vintage look, continue to lose importance. Shiny shoes are becoming increasingly important and will be found more often on the streets this winter. We get more room for a multifaceted design of the shoe factory with the mentioned rivets and buckles. Especially the flatter heels for the modewusste woman of great importance are this year. No longer only high heels, but also shoes with new patterns, colors, and designs work elegantly in this year.
No models are really relieved but also in this year. Therefore, we are not forced to abandon years completely on shoes from the past. Laughed at is in this, as in the past winter seasons, a woman for her shoes. A large selection of current winter models can be found already on some Internet pages of mail-order firms. So, a first insight can be gained, for example, on our site.
Always care should be taken when the importance of various fashion trends, that the fashionable developments, this year taking place, to a even fit. The prettiest shoe, occupied loses with rivets or stones, in effect, if we can’t identify us with this look. It is therefore important to find out first whether the trends should really be made with. In case of an emergency, we can choose also shoes last season or wear more neutral specimens which may not entirely correspond to the style of this season, but complete the rest of the outfit.

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Het'man L., Kaliuha O. Economic fundamentals of stock market regulation in foreign countries // International scientific journal "Internauka". - 2017. - №18.

NOTE: This is version 1.0. Please see the updated version 1.1 in the April 2010 folder.
Bill Hillar, a part-time instructor at the Monterey Institute of International Studies, told students enrolled in his workshops on terrorism and human trafficking about what he described as his own dangerous exploits as a former colonel in the U.S. Army's Special Forces.
He also boasted, they recalled, that the 2008 action movie "Taken," starring Liam Neeson, was based on his life and his daughter's kidnapping by men who wanted to enslave her.
Such claims, along with incidents in which Hillar seemed to borrow material from other people's books, raised suspicions among some of his graduate students about Hillar's resume and background. "He didn't seem to act like a veteran or someone who served so highly in the military," recalled Brian Hubbs, a graduate student and Marine veteran.
So this fall, Hubbs and several other veterans attending the graduate institute began investigating Hillar's resume. And the school now says their suspicions had merit.
Monterey Institute officials said Hillar, who has taught workshops twice yearly at the school since 2005, had claimed to hold a doctorate from the University of Oregon, but a check showed that he had only attended classes there. The institute, which is well-regarded for its foreign language and international relations courses, has been unable to confirm the instructor's claims of military rank and service, officials said.

Thank you all for your sweet comments/tweets/emails on my marathon post yesterday! It means so much to me! I have the best readers! Yesterday, I spent most of the day sitting,napping, and eating.
I’m a bit sore from the marathon and walking down the stairs is quite the accomplishment.
I made a cinnamon roll pumpkin spice muffin for breakfast.
Mix all ingredients in a microwave safe bowl and cook in microwave for 5 minutes.
Top with favorite topping! I used PB2 protein sauce and sugar free maple syrup!
Bee is even getting in on taking pictures of my food.. she is pro.
I spent lots of time just like this.
Even went to church and there was no way I was taking off my compression socks..
Want to know how to wear compression socks to church?
I laughed when I found out I wasn’t the only one who wears compression to church.
Do you ever get sick after a marathon??
Racing lowers your immune system so its common to catch a bug afterward.
I did after my first one and since then I always make sure to take in some Vitamin C after a race.
For dinner I made some butternut squash, green beans and Hake. I always make more then we eat so we have some leftovers for meals to get us through the week. AKA. 2 days.
Squatting may not be in the books tomorrow..
I’ll modify a bit! Specter is a rough workout. Actually that is an understatement.
Its terrible. And I love it.
The Huntsville Marathon AKA “The Full Monte” is a beautiful course! I ran the race with my friend Kenzie, Wendy, Kim and her husband Brian.
We loaded on the bus at about 7am. The race has a late start time at 9am. The past two days have been pretty chilly, stormy and my enthusiasm about the race was dropping.. I was worried the race would be cold.. When we got out of the car, I about got back in.. It was pretty chilly and I was glad I was wearing 9372 layers.
The race director came into the bus to welcome us, wish us good luck and tell us a little bit about the course before we headed to the top.
On the bus Kenzie and I both had our breakfast of oatmeal, and made sure to drink plenty of water!
When we got to the top there was nothing but clear skies! Yes, there was snow on the ground and the grass was frozen..but the sun was shining and it looked to be the perfect race day.
They had a tent with a heater in it at the top. It was about 30 ish degrees at the top so we squeezed in with about 600 of my closest friends.
I really had on 4 layers! Inside the tent I was warm and cozy. There was plenty of “honey buckets” up top so I never really had to wait in a long line to go to the bathroom.
Here are all the GPP peeps that ran the full monte!
They gave us a 20 minute warning to go time and we headed out of the warm tent, dropped our drop bags, jumped around to warm up a bit.
The race started a little later then planned.
I wore my zip jacket, gloves with hand warmers for the first 7 ish miles! I was glad to ditch my jacket but I regretted taking off my gloves then. My fingers and toes were cold till about mile 18. I didn’t care to much because the view was AMAZING! The changing leaves with the snow cap mountains in the backround was absolutely breathtaking. I felt like I was running in a picture.
You can find this video on their website of the Huntsville Marathon in seven minutes!
The Huntsville Course is mostly downhill! It is a significant downhill the first 13 miles and to a gradual downhill at the half way point. Expect gradual small hill at mile 17.The last 6 miles are completely flat.
The Canyon is cool, with a slight headwind. It honestly was perfect race weather. When you get to the last 6 miles you are running past pastures, and homes. The race did a great job by adding, cheerleaders, bands and uplifting signs to help keep your head in the game.
The aid stations were fun, some were dressed up, some even ripped the top of the GU pack for you and the majority of the aid stations held the gatorade and water out for you. Some aid stations even had vaseline sticks they were handing out. There was also oranges and bananas at some. Towards the end one of the aid stations had swedish fish, pickle juice, fruit, pretzels and I think I even saw bagel pieces. The last aid station ran out of cups.. and at that point I was so thirsty! I was glad I had my water bottle on me and that a guy gave out strawberries in front of his house. The bands and cheerleaders along the last few miles were awesome.
A week before this race I had talked myself into maybe not doing it. I have been battling plantar fasciitis for months and it at times is really painful. I knew I wouldn’t do as well as I wanted because of it.
After talking to friends and telling myself,I have done it before and I knew I could do it again. I went for it. I decided to just enjoy the race atmosphere and run the race because I love to run.
I had a goal of 3:45. I was a little ahead of pace according to my race smart bands. The downhill in the first half was perfect, I was able to run a comfortable pace and still keep ahead of schedule. I finished the first half right on pace. At mile 18, my foot started to tighten up and cramp. I slowed down and tried to focus on what was in front of me. At mile 21 I was 10 minutes behind pace and it felt like my foot snapped. I had a sharp pain and came to a complete stop right before an aid station. I walked through the aid station, stretched my foot on a rock and shook it off and kept running. At mile 23 I had fallen even more behind and at this point, I knew I wouldn’t hit my goal and mentally gave up.
T & B were stretching and ready to run it home with me!
As soon as I saw them, they jumped up and ran out to me.They grabbed onto my hands and run to the finish.
Tanner wanted to run through by himself so he let go of my hand and waited till I got across with Bee. I turned around to cheer him through!
He jumped over the finish line and said “MOM! I’m fast like you!” That little guy melts my heart! He even found an old race bib at our house and asked Brent to put it on him for the race.
I didn’t get a PR. It is still in the chase. But I felt great overall besides my dang foot. I am proud of myself for pushing through when I mentally quit when I knew I wouldn’t hit my goal. It’s not about the PR. A marathon is about SO much more then that.
I have some pretty amazing husband and friends that support me.
Overall, I had a great experience, I loved the course and feel like I could be back next year with a PR.
I wouldn’t do anything different. I made sure to stay on top of my fuel and hydration, I had no stomach issues and felt great the whole time. Besides my foot, my legs didn’t quite give out till mile 23. And without having many long runs I think that was pretty good.
Both Kenzie and I followed a GPP training plan! Kenzie PR’d by 17 minutes! We both agreed that the plan was perfect for us. The longest run on the plan was 20 miles. (Which I never did because I ran a half marathon that day instead..) We both felt prepared and ready for the race.
I finished in 4:10 placing 11th in my age division.
If you are looking for a well organized race- start to finish, a beautiful course with a rockin’ downhill. This would be a great course for you.
It was one of my favorite courses!
The winner of the marathon finished in 2:19!!!! That is insane. Amazing. Inspiring.
Marathoners: What is your favorite marathon?
What gets you through those last miles (any distance)?
Today, the twins and I got stuff done today.
I got my 3 mile run done and that was that for the day.
Also, got some work done.
After the workout, and Bee’s dance we headed to the grocery store and the kids were totally stoked about the pile of pumpkins!
The leaves, the cooler ish weather, trail running, and of course pumpkin everything.
Now I get to upload it with music! AKA: Fight with itunes and put a curse on technology.
I also grabbed some new shoes. I could tell that my last mizunos had their last race last weekend.
I picked these babies up at Doboers in Bountiful. Locals: GO there! Dennis (the owner) is very knowledgeable and helpful. Not to mention if you pay in cash you get a discount!
I have been wearing my plantar fasciitis sock for the past two days.. still buggin, but it tends to help a little.
Want to know my favorite running song right now..
What songs do I NEED on my playlist?
I have the Huntsville Marathon this Saturday!
but overall, I trust my training.
Honestly, I didn’t do a 20 mile run. I had one on the schedule but did Big Cottonwood Canyon Half Marathon that weekend instead.. I also split the majority of my long runs into two runs each day just because of that crazy thing we call life.
But then again, I have never done a 20+ mile run in training before..
I’m ready to run though.
It will be beautiful. Downhill. & I’ll probably lose a toenail.
SIDENOTE: This race isn’t full yet so if you need a race soon.. REGISTER!
There is a Full—> Party with me…. Half Marathon, 10 k and 5k!!
My friend Kenzie found these awesome race pace bands! This is a Utah based company, they create the pace bands coordinated to the race course you are doing!
Click on pace bands and from there, select your race and your goal time!
I love this and can’t wait to try it. No matter the distance of every run I think of it as two runs. For example, if I have a 5 mile run. I tell myself I have two 2.5 mile runs.
When I do a Marathon, I take it ONE mile at a time. If I have a goal pace for each mile it will help to focus on that mile and not the 9,382 more there is left.
I’m hoping for a perfect day.
Today I had a two mile run at 70%. I over shot a little bit.. 2.37 but whateve.
After my run, I ran errands- forgot about teaching a boot camp class.. seriously, completely spaced it! I’m losing it y’all…. Picked up the twinners from pre-school and headed home for lunch.
I haven’t been posting recipes lately..
I have figured out my nutrition and its simple.
But it works for me. I have been craving something yummy soon, so I’'ll be coming up with something snazzy for ya!
Sometimes (more like always) for lunch I make my whole meal in the same pan.
Hate dishes? This works just fine!
Mahi Mahi plus yellow squash and asparagus!
Hot and steamy = awesome pictures.
And just because I love this little golf man.
Ladies, here is some eye candy.
Do you run with a pace band?
Marathoners how many 20 + runs do you do?
Fall is coming. Enjoy it.
This morning I headed straight to body pump. It was a sweaty grand time.
I haven’t taught on a Saturday for awhile due to races and vacation. It felt great to hang out with the Saturday crew! The class was packed and we all left with major noodle legs and arms.
After pump,I got a text from my friend Tara asking if I wanted to go for a trail run.
It was such a beautiful hike/run. The leaves are starting to change! I have to go up in a few weeks and that entire view will be yellow, red and orange!
I made it home right in time for a park date with my family! We grabbed some plates and palates and headed to the park!
Brent headed to Provo for a football game and I hung out with the kiddos and watched bee catch potato bugs and store them in her bike.
Fall is coming. Enjoy it.
Middle of week dance party!
Something about this video just makes me happy! “Life is meant to be enjoyed”!
I woke up this morning and headed to the GPP. I grabbed a quick pre workout snack to get me through the morning. It was just a slice of Ezekiel bread with Nuttzo butter and Rasberries and a quest bar.
I love this quote at GPP and having it lit up in the morning just made it that much better.
“Without strength you have none to give”!
After coaching a couple classes myself I got to tackle this beast.
Yep, 200 reps. Once you started an exercise you had to finish all 200 reps before moving on to the next exercise. We timed each exercise. Some of these took me a little longer then I thought but I caught myself talking a little bit more.. oops.
After the workout we went and visited Brent at work and ran a couple errands before heading home. I was more then ready for lunch and while my lunch was cooking I ate a sweet potato and quite a few raspberries with nuttzo.---> Pretty much the best snack ever!
When my fish was done I sat down to enjoy a meal, not out of a plastic bag or tupperware.
That is right. I put it on a actual plate!
I love fish lately! I had Mahi Mahi with roasted red pepper hummus and sprinkled with Mrs. Dash (Chicken flavor) and asparagus to finish off lunch.
Then we played dress up.
This little girl LOVES make up. Especially blush. I love her.
I had easy miles on schedule today. I procrastinated it like a pro.
I finally headed out and got it done! I never run with my calf sleeves. Not sure if I could tell a difference while running but felt good. Finished five in 46:32. Texting and running is not recommended for training runs.. or maybe I’m not a great multi-tasker when it comes to that.
I’m a huge fan of Pandora. I’m not great at downloading music to my iphone and I love variety so I usually just depend on Pandora for all my training runs. I have only a select few that I use during runs.
PS. Pandora one is an amazing thing. It’s $3.99 a month to avoid commercials and it’s worth it. Nothing is worse then getting ready to charge up a hill and a commercial about birth control or health insurance comes up.
I found a new favorite station that I started playing at the gym and during my run today. I love it!
I even listen to “Today’s Comedy Radio” if I’m in need for a good laugh while running.
Do you have a favorite Pandora station?
Fall is coming. Enjoy it.

Shopping for home insurance in Elliott, IA doesn’t have to be difficult. Simply enter your Zip Code at the top of this page and you will be presented with the list of the top recommended insurance companies in your area. Compare quotes from these carriers and you will be on your way to saving on your homeowners coverage premium.
When it comes to homeowner’s insurance in Elliott, IA, there are quite a few different factors that can affect how much you have to pay. Understanding what these factors are can give you a better idea of how Iowa insurance companies come up with the quotes that they give you.
All of these factors come into play when getting Elliott, IA homeowner’s insurance quotes. If you want to keep your costs as low as possible, consider choosing a policy with less coverage or with a higher deductible. Just make sure that you fully understand how these decisions will affect you if you ever need to file a claim. You may find it more beneficial to go for a policy that offers more coverage or a lower deductible so that you don’t have to come up with a lot of money on your own if something does eventually happen to your home.
To get the best savings on your Elliott, Iowa coverage for your home, make sure to use our comparison tool. Enter your Zip Code below and get the list of the best Iowa insurers.
A house is a higher stage of accountability, so you have to have the right insurance. But, if you are unfamiliar with property owner's insurance coverage, there may possibly be some things you do not realize. As you compare insurers, procedures and packages, keep in mind these simple ideas.
Save cash on your homeowner's insurance policies by not acquiring items that are possibly injurious. Creating a swimming pool or buying a trampoline can raise your once-a-year premium by as a lot as ten per cent or even much more. Alternatively, visit the neighborhood pool or playground and get the same enjoyment for a reduced price.
Homeowner's insurance shouldn't be up for consideration, you need to go out and get it. You could get rid of everything, in the celebration of an unexpected emergency, without this insurance policy. Insurance policies might be a prerequisite if you are mortgaging your property.
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Browsing the Web from your wristwatch may not be ideal, but it’s now completely possible if you’re using the Galaxy Gear. Tech savvy tinkerers have developed the first custom ROM for Samsung’s watch.
The hack comes courtesy of XDA forum member fOmey, who posted a ROM that bypasses a few of Samsung’s limitations to run third-party apps, widgets and wallpapers. The ROM also enables the Galaxy Gear to connect to the Web via any nearby smartphone that supports Bluetooth tethering.
Screenshots of the custom ROM running on a Galaxy Gear show the Google homepage on the watch’s 1.6-inch screen, new live wallpapers, weather and time widgets. It’s not clear how smoothly the ROM works, but the XDA post provides full instructions along with FAQs.
In our review, we gave the Galaxy Gear high marks for its clear call quality and battery life, but lamented it for its limited compatibility and lack of Facebook and Twitter apps. Despite generally lukewarm reviews of the Gear, developers appear to be fiddling with the watch to expand its capabilities. We look forward to seeing what else they create.

CH-001 Plain Oval, Size 20cm x 16.0cm x 4.5cm, Example Snakeskin Black.
CH-002 Curved Oval, Size 20cm x 16.5cm x 4.5cm, Example Snakeskin Blue.
CH-003 Centre Banded Oval, Size 20cm x 16.5cm x 5.3cm, Example Snakeskin Green.
CH-004 Double Banded Oval, Size 21cm x 17.5cm x 5.3cm, Example Blue + White.
CH-005 Oval with Rim, Size 21cm x 17.5cm x 5.3cm, Example Blue.
CH-006 Small Oval, Size 19cm x 13.5cm x 5.0cm, Example Snakeskin Black.
CH-007 Medium Oval, Size 25cm x 17.5cm x 5.5cm, Example Snakeskin Brown.
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CH-009 Small Oval with Rim, Size 19.8cm x 14.5cm x 5.0cm, Example Mustard.
CH-010 Medium Oval with Rim, Size 26cm x 19cm x 5.5cm, Example Fudge.
CH-011 Large Oval with Rim, Size 29.5cm x 21.5cm x 6.0cm, Example Grey.
CH-012 Handmade Oval-Foot Style ‘A’, Size 24.5cm x 17.5cm x 4.5cm, Example Mustard.