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 Skip Navigation LinksMath Help > Math Puzzles > A Two Player Game

A Two-Player Game related to Wythoff's Game and Beatty Sequences

Let's play a game.  I'll be the computer, and you be the human, OK?  I'll hand you a slip of paper on which will be printed two numbers -- all numbers are nonnegative integers.  Then you can reduce one or both of the two numbers by any positive integer amount, but you can't make either number negative, and then you can hand me back the slip of paper.  We take turns reducing one or both of the numbers until one of us reduces both numbers to 0, winning the game.

What is a good strategy for winning the game?

Let's play while you think about your strategy.  I'm handing you this card:

45, 17
Now you can reduce  The first number by from 45 to

 and/or 

The second number from 17 to

Source: Wythoff's Game 

Click here for the answer.

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