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JeeJee
Canada5652 Posts
You vs me. An even numer of coins (potentially different denominations) are arranged in a line between us, going left-to-right. We are going to play the following game: We take turns taking a coin from either end of the coin line. The game ends when there are no more coins. The winner is the one whose little pile of coins at the end is worth more than the other's. Simple. You go first. Devise a strategy such that your pile at the end will always at least match my pile in value. GL!  | ||
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onmach
United States1241 Posts
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ieatkids5
United States4628 Posts
if all the denominations are the same, then just pick whatever any other scenario, add up every other number starting at one end, then add up every other number starting from the other end. whichever side you start on that has a greater sum, start picking from that side. example: 43472191 4+4+2+9=19 3+7+1+1=12 start picking from the side with the 4. your opponent has to take the 3 because if he takes the 1, then you will take the 9. after he takes the 3, take the 4. he will take the 7. take the 2. he takes the 1. you take the 9. another example: 27261192 2+2+1+9=14 7+6+1+2=16 start from the right side and take the 2. your opponent will take the 9 because you will take it if he doesnt. take the 1. opponent will take next 1 because he cannot take the 2 on the left (or you will take the 7. take the 6. opponent takes the 2. take the 7. edit - updated with examples | ||
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onmach
United States1241 Posts
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JeeJee
Canada5652 Posts
On February 19 2010 01:55 ieatkids5 wrote: 11111111 if all the denominations are the same, then just pick whatever any other scenario, add up every other number starting at one end, then add up every other number starting from the other end. whichever side you start on that has a greater sum, start picking from that side. example: 43472191 4+4+2+9=19 3+7+1+1=12 start picking from the side with the 4. your opponent has to take the 3 because if he takes the 1, then you will take the 9. after he takes the 3, take the 4. he will take the 7. take the 2. he takes the 1. you take the 9. another example: 27261192 2+2+1+9=14 7+6+1+2=16 start from the right side and take the 2. your opponent will take the 9 because you will take it if he doesnt. take the 1. opponent will take next 1 because he cannot take the 2 on the left (or you will take the 7. take the 6. opponent takes the 2. take the 7. edit - updated with examples i assume you re-calculate these 2 values every time it is your turn? edit @onmach which example shows inadequacy of your strategy? curious.. | ||
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ieatkids5
United States4628 Posts
On February 19 2010 04:48 JeeJee wrote: i assume you re-calculate these 2 values every time it is your turn? edit @onmach which example shows inadequacy of your strategy? curious.. heh oops yes  | ||
Daigomi
South Africa4316 Posts
You add the value of all the odd numbered coins (coin #1, #3, etc) and all the even numbered coins (coin #2, #4, etc) together. If the odd numbered coins total the highest, you start on the left. If the even numbered coins have the highest total, you start on the right. After that you just pick on the same side as your opponent does every turn. | ||
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