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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
$begingroup$
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
combinatorics
$endgroup$
add a comment |
$begingroup$
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
combinatorics
$endgroup$
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
add a comment |
$begingroup$
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
combinatorics
$endgroup$
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
combinatorics
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
add a comment |
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
add a comment |
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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