Ch8_tictactoe magic

# Ch8_tictactoe magic - Chapter 8 TicTacToe Magic Three...

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TicTacToe Magic Three simple games are related in a surprising way. The ﬁrst of the three games is Pick15. Harold Stark, who was then at the University of Michigan, told me about the game in the late 1960s. I suspect that this is the ﬁrst time you have heard of it. The game involves two players. You start by listing the single digit numbers from 1 to 9. You then take turns selecting numbers from the list, attempting to acquire three numbers that add up to 15. Each number can be chosen only once. You may eventually acquire more than three numbers, but you must use exactly three of them to total 15. If neither player can achieve the desired total, the game is a draw. For example, suppose that Green and Blue are playing. They start with the list. List : 1 2 3 4 5 6 7 8 9 Green : Blue : Suppose Green has the ﬁrst move and chooses 8. Then Blue chooses 4 and Green chooses 2. Now Blue should respond by choosing 5 to prevent Green from getting 2 + 5 + 8 = 15. Here is the situation after the ﬁrst two rounds. List : 1 2 / 3 4 / 5 / 6 7 8 / 9 Green : 2 8 Blue : 4 5 Copyright c ± 2009 Cleve Moler Matlab R ± is a registered trademark of The MathWorks, Inc. TM

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## This note was uploaded on 10/11/2011 for the course MTHSC 365 taught by Professor Adams during the Spring '11 term at Clemson.

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Ch8_tictactoe magic - Chapter 8 TicTacToe Magic Three...

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