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What is the maximum number of Amazons that can be placed on a 5x5 . . . Five amazons cannot be placed on the board, because there would need to be one in every row and column Whichever amazon occupies the middle row attacks all squares in columns adjacent to its own, preventing them from being filled Four Amazons can, however, be placed like so: Showing that this is the only solution takes a little casework, but placing an Amazon on either diagonal quickly
strategy - 4x4 Tic-tac-toe variant where three (or four) in a row wins . . . Warmup question 1: Let’s consider the following variant of Tic-tac-toe which is played on the following 4x4 grid The rules are the same as standard Tic-tac-toe and the goal is still to get three in a row without any intervening empty squares or squares marked by the other player Getting four in a row is also a win Assume Player 1 marks with an X and Player 2 with an O If both players
Domino tiling on 8x8 checkerboard with four squares removed Here is my attempt at a proof First I'll prove a useful set of shapes that can be covered by dominoes when two opposite-coloured squares are removed Take any polyomino, a shape made of square units, joined edge to edge If you split its units into 2x2 smaller squares, then there will be a Hamiltonian cycle, i e a closed loop path that visits all the small squares It is easiest to see in a
Creating the hardest 6x6 maze - Puzzling Stack Exchange You are given an empty 6x6 grid You are allowed to paint some of its cells as walls (black), while the remaining cells stay empty (white) A robot is programmed to start in the top-left corner of