Subtraction Game with two numbers

 

 

Start with two numbers; letís say 9 and 14. Each turn a player can subtract 1, 2 or 3 from one of the numbers. The one who makes the last move wins.

 

We find the winning strategy by finding the key positions. What are the key positions for a two numbers subtraction game ?

 

If one of the numbers reaches zero, the game would become a one number subtraction game. So the position (0, n) is a key position if and only if

††††††††††††††††††††††† n mod 4 = 0

 

What are the other key positions?

 

(Follow the Power Point presentation to find out more ÖYou can use OpenOffice to read it.

It looks better in presentation format. If you donít have the presentation programs, try pdf file.)

 

 

Advanced Topic

 

Read on if you know what does n mod t = m mod t mean.

 

 

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