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Picking coins from two piles


Binary manipulation gamePythagorean coinsTwo chessmasters at workPedro's pawn gameNon-Pythagorean coins (Part 1)Non-Pythagorean coins (Part 2)Cristiano Ronaldo's soccer puzzleWord-making gameIntroducing: Sudoku-JanpuThree coins for the fair king













13












$begingroup$


It is a variation of the game of Nim.



The rules are :



The game is played with two piles of coins. Initially, the first pile contains N coins and the second one contains M coins.



There are two players A and B. They alternate turns.



A plays first. On each turn, the current player must choose one pile and remove a positive number of coins (not exceeding the current number of coins on that pile) from it.



It is only allowed to remove X coins from a pile if the number of coins in the other pile divides X.



The player that takes the last coin from any pile wins.



Both players play optimally.



For a given N and M, devise a procedure to find the winner of the game










share|improve this question











$endgroup$







  • 1




    $begingroup$
    In other words "X is a multiple of coins on the other pile". If one of the pile becomes empty the game is over.
    $endgroup$
    – user60166
    May 8 at 10:51











  • $begingroup$
    Sorry, I removed my comment. I didn't see the game ended at the first empty pile, and had normal Nim games in mind where all piles become empty.
    $endgroup$
    – Jaap Scherphuis
    May 8 at 10:54










  • $begingroup$
    This post has been locked, as it is taken from an ongoing contest. For more information see our policy on Questions from Ongoing Contests. It comes from the Code Chef May Long Challenge, ending 13-May at 15:00 IST. I don't plan to keep tabs on this question until then, so if OP (or someone else) is interested enough in having it unlocked, please flag it for moderator attention once the contest has ended.
    $endgroup$
    – Rubio
    May 8 at 14:59















13












$begingroup$


It is a variation of the game of Nim.



The rules are :



The game is played with two piles of coins. Initially, the first pile contains N coins and the second one contains M coins.



There are two players A and B. They alternate turns.



A plays first. On each turn, the current player must choose one pile and remove a positive number of coins (not exceeding the current number of coins on that pile) from it.



It is only allowed to remove X coins from a pile if the number of coins in the other pile divides X.



The player that takes the last coin from any pile wins.



Both players play optimally.



For a given N and M, devise a procedure to find the winner of the game










share|improve this question











$endgroup$







  • 1




    $begingroup$
    In other words "X is a multiple of coins on the other pile". If one of the pile becomes empty the game is over.
    $endgroup$
    – user60166
    May 8 at 10:51











  • $begingroup$
    Sorry, I removed my comment. I didn't see the game ended at the first empty pile, and had normal Nim games in mind where all piles become empty.
    $endgroup$
    – Jaap Scherphuis
    May 8 at 10:54










  • $begingroup$
    This post has been locked, as it is taken from an ongoing contest. For more information see our policy on Questions from Ongoing Contests. It comes from the Code Chef May Long Challenge, ending 13-May at 15:00 IST. I don't plan to keep tabs on this question until then, so if OP (or someone else) is interested enough in having it unlocked, please flag it for moderator attention once the contest has ended.
    $endgroup$
    – Rubio
    May 8 at 14:59













13












13








13


1



$begingroup$


It is a variation of the game of Nim.



The rules are :



The game is played with two piles of coins. Initially, the first pile contains N coins and the second one contains M coins.



There are two players A and B. They alternate turns.



A plays first. On each turn, the current player must choose one pile and remove a positive number of coins (not exceeding the current number of coins on that pile) from it.



It is only allowed to remove X coins from a pile if the number of coins in the other pile divides X.



The player that takes the last coin from any pile wins.



Both players play optimally.



For a given N and M, devise a procedure to find the winner of the game










share|improve this question











$endgroup$




It is a variation of the game of Nim.



The rules are :



The game is played with two piles of coins. Initially, the first pile contains N coins and the second one contains M coins.



There are two players A and B. They alternate turns.



A plays first. On each turn, the current player must choose one pile and remove a positive number of coins (not exceeding the current number of coins on that pile) from it.



It is only allowed to remove X coins from a pile if the number of coins in the other pile divides X.



The player that takes the last coin from any pile wins.



Both players play optimally.



For a given N and M, devise a procedure to find the winner of the game







combinatorics






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited May 8 at 10:44

























asked May 8 at 10:30







user60166














  • 1




    $begingroup$
    In other words "X is a multiple of coins on the other pile". If one of the pile becomes empty the game is over.
    $endgroup$
    – user60166
    May 8 at 10:51











  • $begingroup$
    Sorry, I removed my comment. I didn't see the game ended at the first empty pile, and had normal Nim games in mind where all piles become empty.
    $endgroup$
    – Jaap Scherphuis
    May 8 at 10:54










  • $begingroup$
    This post has been locked, as it is taken from an ongoing contest. For more information see our policy on Questions from Ongoing Contests. It comes from the Code Chef May Long Challenge, ending 13-May at 15:00 IST. I don't plan to keep tabs on this question until then, so if OP (or someone else) is interested enough in having it unlocked, please flag it for moderator attention once the contest has ended.
    $endgroup$
    – Rubio
    May 8 at 14:59












  • 1




    $begingroup$
    In other words "X is a multiple of coins on the other pile". If one of the pile becomes empty the game is over.
    $endgroup$
    – user60166
    May 8 at 10:51











  • $begingroup$
    Sorry, I removed my comment. I didn't see the game ended at the first empty pile, and had normal Nim games in mind where all piles become empty.
    $endgroup$
    – Jaap Scherphuis
    May 8 at 10:54










  • $begingroup$
    This post has been locked, as it is taken from an ongoing contest. For more information see our policy on Questions from Ongoing Contests. It comes from the Code Chef May Long Challenge, ending 13-May at 15:00 IST. I don't plan to keep tabs on this question until then, so if OP (or someone else) is interested enough in having it unlocked, please flag it for moderator attention once the contest has ended.
    $endgroup$
    – Rubio
    May 8 at 14:59







1




1




$begingroup$
In other words "X is a multiple of coins on the other pile". If one of the pile becomes empty the game is over.
$endgroup$
– user60166
May 8 at 10:51





$begingroup$
In other words "X is a multiple of coins on the other pile". If one of the pile becomes empty the game is over.
$endgroup$
– user60166
May 8 at 10:51













$begingroup$
Sorry, I removed my comment. I didn't see the game ended at the first empty pile, and had normal Nim games in mind where all piles become empty.
$endgroup$
– Jaap Scherphuis
May 8 at 10:54




$begingroup$
Sorry, I removed my comment. I didn't see the game ended at the first empty pile, and had normal Nim games in mind where all piles become empty.
$endgroup$
– Jaap Scherphuis
May 8 at 10:54












$begingroup$
This post has been locked, as it is taken from an ongoing contest. For more information see our policy on Questions from Ongoing Contests. It comes from the Code Chef May Long Challenge, ending 13-May at 15:00 IST. I don't plan to keep tabs on this question until then, so if OP (or someone else) is interested enough in having it unlocked, please flag it for moderator attention once the contest has ended.
$endgroup$
– Rubio
May 8 at 14:59




$begingroup$
This post has been locked, as it is taken from an ongoing contest. For more information see our policy on Questions from Ongoing Contests. It comes from the Code Chef May Long Challenge, ending 13-May at 15:00 IST. I don't plan to keep tabs on this question until then, so if OP (or someone else) is interested enough in having it unlocked, please flag it for moderator attention once the contest has ended.
$endgroup$
– Rubio
May 8 at 14:59










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