There are two piles of rocks, each with 7 rocks. Consider the game with two players where: in one turn you can take any amount of rocks, but only from one pile. The loser is the one who has no rocks left to take.
Two people take turns placing knights on a chessboard such that the knights cannot attack each other. The loser is the player who cannot make a move. Which player wins the game, if the right strategy is used?
Two people take turns placing kings on squares of a \(9 \times 9\) chessboard such that the kings cannot attack each other. The loser is the player who cannot make a move. Which player wins the game, if the right strategy is used?
a) Two in turn put bishops in the cells of a chessboard. The next move must beat at least one empty cell. The bishop also beats the cell in which it is located. The player who loses is the one who cannot make a move.
b) Repeat the same, but with rooks.
There is a board of \(10 \times 10\) squares. Consider the game with two players where: in one turn a player is allowed to cover any two adjacent squares with a domino (a \(1 \times 2\) rectangle) so that the domino doesnt cover another domino. The loser is the one who cannot make a move. Which player would win, if the right strategy was used?
In each square of an \(11\times 11\) board there is a checker. Consider the game with two players where: in one move a player is allowed to take any amount of adjacent checkers from the board, as long as they checkers are in the same vertical column or in the same horizontal row. The winner is the player who removes the last checker. Which player wins the game?
There are two piles of rocks: one with 30 rocks and the other with 20 rocks. In one turn a player is allowed to take any number of rocks but only from one of the piles. The loser is the player who has no rocks left to take. Who would win in a two player game, if the right strategy is used?
There are twenty dots distributed along the circumference of circle. Consider the game with two players where: in one move a player is allowed to connect any two of the dots with a chord (aline going through the inside of the circle), as long as the chord does not intersect those previously drawn. The loser is the one who cannot make a move. Which player wins?
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?
Two people take turns drawing noughts and crosses on a \(9 \times 9\) grid. The first player uses crosses and the second player uses noughts. After they finish, the number of rows and columns where there are more crosses than noughts are counted, and these are the points which the first player receives. The number of rows and columns where there are more noughts than crosses are the second player’s points. The player who has the most points is the winner. Who wins, if the right strategy is used?