Problema Solution
The Game of Take
The Game of Take is a game played by two players with two
heaps of coins (or stones or beans). The rules of the game are
as follows:
(1) The players alternate turns (let us call the player who
makes the 1st move I and then call the other player II).
(2) Each player, when it is his or her turn, selects one of the
heaps and removes at least one of the coins from the
selected heap. (The player may take all of the coins from
the selected heap, thereby leaving an empty heap, which is
now \out of play.")
The last player to make a move|that is, the player who takes
the last coin(s)|is the winner.
Question: Can the winner be determined right at the start of
the game? Justify your answer.
Answer provided by our tutors
The Game of Take
The Game of Take is a game played by two players with two
heaps of coins (or stones or beans). The rules of the game are
as follows:
(1) The players alternate turns (let us call the player who
makes the 1st move I and then call the other player II).
(2) Each player, when it is his or her turn, selects one of the
heaps and removes at least one of the coins from the
selected heap. (The player may take all of the coins from
the selected heap, thereby leaving an empty heap, which is
now \out of play.")
The last player to make a move|that is, the player who takes
the last coin(s)|is the winner.
Question: Can the winner be determined right at the start of
the game? Justify your answer.
Yes, it can be determined if you know the number of stones or coins. if the number is even then player 2 will win and if it is odd, then player 1 will win..