The game of 31 was a favourite of con artists who rode the railroads in days of yore. The game
is played with a deck of 24 cards: four labelled each of 1, 2, 3, 4, 5, 6. The cards in the deck are
visible to both players, who alternately withdraw one card from the deck and place it on a pile.
The object of the game is to be the last player to lay a card such that the sum of the cards in
the pile does not exceed 31. Your task is to determine the eventual winner of a partially played
game, assuming each player plays the remainder of the game using a perfect strategy.
For example, in the following game player B wins:

]]> The input will consist of several lines; each line consists of a sequence of zero or more digits
representing a partially completed game. The first digit is player A’s move; the second player
B’s move; and so on. You are to complete the game using a perfect strategy for both players
and to determine who wins.

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For each game, print a line consisting of the input, followed by a space, followed by A or B to
indicate the eventual winner of the game.

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One of the central ideas behind much cryptography is that factoring large numbers is computationally
intensive. In this context one might use a 100 digit number that was a product of two 50 digit prime
numbers. Even with the fastest projected computers this factorization will take hundreds of years.
You don’t have those computers available, but if you are clever you can still factor fairly large numbers.

]]> The input will be a sequence of integer values, one per line, terminated by a negative number. The
numbers (other than the terminator) will be greater than 0 and less than 2⁶² .

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Each positive number from the input must be factored and all factors (other than 1) printed out. The
factors must be printed in ascending order with 4 leading spaces preceding a left justified number, and
followed by a single blank line.

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A Fibonacci sequence is calculated by adding the previous two members of the sequence, with
the first two members being both 1.
f (1) = 1, f (2) = 1, f (n > 2) = f (n − 1) + f (n − 2)
Your task is to take a number as input, and print that fibonacci number.

]]> 100

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354224848179261915075

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No generated fibonacci number in excess of 1000 digits will be in the test data, i.e. f (20) = 6765
has 4 digits.

]]> You are to find all the two-word compound words in a dictionary. A two-word compound word is a
word in the dictionary that is the concatenation of exactly two other words in the dictionary.

]]> Standard input consists of a number of lowercase words, one per line, in alphabetical order. There will
be no more than 120,000 words.

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Your output should contain all the compound words, one per line, in alphabetical order.

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I’m king of a house! And, what’s more, beyond that,
I’m king of a blueberry bush and a cat!
I’m Yertle the Turtle! Oh, marvelous me!
For I am the ruler of all that I see!"
The Problem
Yertle has determined that the number of objects he can see, and hence rule, depends on the height of his
throne. Your task, as Minister of Computing and Vertigo (a new combined Super Ministry), is to
determine which objects Yertle would see should he build his throne to a particular height.
Standard input consists of:
A floating point number on a line by itself, specifying the diameter of Yertle’s planet in "flipper
lengths".
A line containing three floating point numbers: the height of Yertle’s throne (in flipper lengths), the
latitude of Yertle’s throne (between -90 and +90 degrees), the longitude of Yertle’s throne (between 0
and 360 degrees).
Several lines, each containing three floating point numbers and a string of alphabetic and space
characters. Each line indicates the height, latitude, longitude and name of an object on the surface of
Yertle’s planet. The last line is indicated by the end of standard input.
All distances are in flipper lengths, and all latitudes and longitudes are in degrees. Floating point values
are formatted as a string of decimal digits with an optional decimal point and sign. The fields in the input
are separated by exactly one space character. You may assume that no object hides another; only the
horizon limits Yertle’s view.
Standard output consists of:
The list of objects whose tops are visible to Yertle, in alphabetical order.

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