Question

The game takes place on an infinite plane. One player moves the wolf, and another player moves K sheep. After the wolf's move, one of the sheep makes a move, then the wolf again, and so on. In one move, the wolf or a sheep cannot move more than one meter in any direction. Can the wolf always catch at least one sheep, regardless of the initial positions?

Difficulty level (1 very easy - 10 very hard): 8

Combinatorics -> Combinatorial Geometry Combinatorics -> Invariants Geometry -> Plane Geometry Logic -> Reasoning / Logic Proof and Example -> Constructing an Example / Counterexample Minimum and Maximum Problems / Optimization Problems

Sources:

Tournament of Towns, 1980-1981, Spring, Main Version, Grades 11-12 Question 2

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