Chess

There are numerous chess puzzles present which vary in their difficulty level. The traditional ones will show a legal position and a condition with White or Black to move first and force (check)mate by a certain number of moves. Alternatively, the solver has to force a win in material(easier) or draw by stalemate or position(harder). By tradition also, the first move or keymove will not be a check, but an innoculous move, to further increase the difficulty level. Naturally, the greater number of moves allowed, the more possibilities there are to consider and hence harder the solution. Similiarly, more pieces on the board also increases the difficulty, as each piece must serve some purpose. However, these puzzles tend to require a chess-trained mind and will thus kill a lot of braincells for most people. Hence I will present some more thought provoking and interesting ones instead.

(1) Catch The Black King

The only pieces on the board are a black king on a corner square and a white knight on the corner square directly opposite. Players alternate moves. White wins if the knight can check the king within twenty moves, else Black wins. Should you play White or Black, and should you start first?

Discussion - Black will always win, regardless of who starts and how many moves White gets. The knight is known as a square-root-13 mover, and will always end on a square of opposite colour from its starting square. Noting this, the black king only has to move onto a square of colour opposite to that of the knight(and not in check) whenever it comes within range. This makes it impossible for the knight to check the king on its next move.

(2) Dominoes and Chessboard

You have a chessboard with the two opposite black corners removed and 31 dominoes, each the size of two squares. How many unique ways are there to cover the entire chessboard with the 31 dominoes?

Discussion - It is impossible to cover the entire chessboard with the dominoes due to the removal of the two black corner squares. Each domino takes up two adjacent squares - one white, one black. However, there are 32 white squares and 30 black squares.

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