Unique differences
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Susam Pal
Jul 10, 2011, 1:57:28 AM7/10/11
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Source: http://cotpi.com/p/12/
Four friends, Alice, Bob, Charlie and Dave, meet one Sunday afternoon
to play a game of cards. There are 35 cards, each labelled with a
unique positive integer between 1 and 35, inclusive. They are placed
face-up on a table. In each round, each player takes turns removing
one card from the table.
In the first round, a player is allowed to remove any card. From the
second round onwards, a player is allowed to remove any card labelled
with a number which is the difference of the numbers of two cards that
have been removed before. The game ends when nobody can remove a card.
The last one to remove a card from the table wins.
In each round, Alice takes the first turn, followed by Bob, Charlie
and David, in that order. Alice did not remove a card with a multiple
of 7 in the first round. Who can definitely win the game?
Four friends, Alice, Bob, Charlie and Dave, meet one Sunday afternoon
to play a game of cards. There are 35 cards, each labelled with a
unique positive integer between 1 and 35, inclusive. They are placed
face-up on a table. In each round, each player takes turns removing
one card from the table.
In the first round, a player is allowed to remove any card. From the
second round onwards, a player is allowed to remove any card labelled
with a number which is the difference of the numbers of two cards that
have been removed before. The game ends when nobody can remove a card.
The last one to remove a card from the table wins.
In each round, Alice takes the first turn, followed by Bob, Charlie
and David, in that order. Alice did not remove a card with a multiple
of 7 in the first round. Who can definitely win the game?
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