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Euclid's Game starts with two unequal positive numbers on the board. For this problem, assume that permissible starting numbers are in the range [1, 50]. Two players move in turn. On each move, a player has to write on the board a positive number equal to the difference of two numbers already on the board; this number must be different from all the numbers already written on the board. The player who cannot move loses the game. a. Give three examples of a 'game tree' for Euclid's Game for any pair of numbers you choose. b. Should you choose to move first or second in this game?

Euclid's Game starts with two unequal positive numbers on the board. For this problem, assume that permissible starting numbers are in the range [1, 50]. Two players move in turn. On each move, a player has to write on the board a positive number equal to the difference of two numbers already on the board; this number must be different from all the numbers already written on the board. The player who cannot move loses the game. a. Give three examples of a 'game tree' for Euclid's Game for any pair of numbers you choose. b. Should you choose to move first or second in this game?

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
Problem 7P
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2. Euclid's Game starts with two unequal positive numbers on the board. For this problem, assume that permissible starting numbers are in the range [1, 50]. Two players move in turn. On each move, a player has to write on the board a positive number equal to the difference of two numbers already on the board; this number must be different from all the numbers already written on the board. The player who cannot move loses the game. a. Give three examples of a 'game tree' for Euclid's Game for any pair of numbers you choose. b. Should you choose to move first or second in this game?
Transcribed Image Text:2. Euclid's Game starts with two unequal positive numbers on the board. For this problem, assume that permissible starting numbers are in the range [1, 50]. Two players move in turn. On each move, a player has to write on the board a positive number equal to the difference of two numbers already on the board; this number must be different from all the numbers already written on the board. The player who cannot move loses the game. a. Give three examples of a 'game tree' for Euclid's Game for any pair of numbers you choose. b. Should you choose to move first or second in this game?
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