2-player game: taking turns choosing from pile of counters

lakers2

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Nov 21, 2008
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You will be given a set of numbers to play this game. Two players start with a pile of counters and take turns choosing numbers from their set (repeats are allowed) to remove from the pile. The first person to leave 0 counters wins. For example, if you are given numbers 1,2,3,4, we can see that starting with a number not divisible by 5, the second player can force a win by always bringing the running total to a multiple of 5.

Hint: suppose the numbers in your set were 1,3. Then work “backwards” from the lowest numbers to see what are the winning and losing positions. For example, in this case, 1 would be a winning number since that player could remove 1 counter. 2 is a losing number, since the player with that number can only remove 1, leaving a winning number for her opponent. 3 is a winning number, since that player can remove 3. And for is a losing number, since that player can remove 1 or 3, leaving a winning number for her opponent. If you continue with this example, you will begin to see that odd numbers are losing numbers, and even numbers are winning numbers. Your problem will most likely have a more complicated analysis than this though!

Your set of numbers is: 1,4,6,10 (You can only take these numbers away from the counters; you can’t take 2, 3, 5, 7, 8, or 9)

a. Find a winning strategy if the game begins with 15 counters in the pile.
b. Find and explain the winning strategy if the game begins with 35 counters in the pile.
c. Find and explain the winning strategy if the game begins with any number counters in the pile.
 
Re: math game problem please help

Hi, Lakers. What, specifically are you having trouble with? If you read the post "Read Before Posting," you would know that we really don't do people's assignments for them. If you have a specific question about these assignments, please ask it, and you will find that we will be all over it. Be as complete as possible in showing what work you have done this far, and try to spell out exactly where you're having difficulty. Thanks.
 
Lakers, changing it a bit to whoever picks the last one loses, can you
see that you're sure to win if you leave 5 counters after one of your moves?
 
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