TOT 011 1981 Spring J5 S2 infinite plane, 1 wolf, K sheep, game
Source:
August 17, 2019
combinatoricsgamegame strategy
Problem Statement
a) A game is played on an infinite plane. There are fifty one pieces, one “wolf” and “sheep”. There are two players. The first commences by moving the wolf. Then the second player moves one of the sheep, the first player moves the wolf, the second player moves a sheep, and so on. The wolf and the sheep can move in any direction through a distance of up to one metre per move. Is it true that for any starting position the wolf will be able to capture at least one sheep?b) A game is played on an infinite plane. There are two players. One has a piece known as a “wolf”, while the other has pieces known as “sheep”. The first player moves the wolf, then the second player moves a sheep, the first player moves the wolf again, the second player moves a sheep, and so on. The wolf and the sheep can move in any direction, with a maximum distance of one metre per move. Is it true that for any value of there exists an initial position from which the wolf can not capture any sheep?PS. (a) was the junior version, (b) the senior one