Problem #PRU-30451

Problems Set theory and logic Algorithm Theory Game Theory Symmetric strategies

Problem

Consider a rectangular parallelepiped with size a) \(4 \times 4 \times 4\); b) \(4 \times 4 \times 3\); c) \(4 \times 3 \times 3\), made up of unit cubes. Consider the game with two players where: in one turn a player is allowed to pierce through any row with a long wire, as long as there is at least one cube in the row with no wire. The loser is the player who cannot make a move. Who would win, if the right strategy is used?