Solution. The puzzle is impossible to complete. A domino placed on the chessboard will always cover one white square and one black square. If the two black corners are removed instead, then 32 white squares and 30 black squares remain, so it is again impossible.
What does functional Fixedness mean in psychology?
Functional fixedness is the inability to realize that something known to have a particular use may also be used to perform other functions. When one is faced with a new problem, functional fixedness blocks one’s ability to use old tools in novel ways. Overcoming functional…
Can an 8×8 chessboard with an odd number of squares removed be tiled with 2×1 dominos?
No, it’s not possible. Two diagonally opposite squares on a chess board are of the same color. Therefore, when these are removed, the number of squares of one color exceeds by 2 the number of squares of another color. However, every piece of domino covers exactly two squares and these are of different colors.
What’s the problem with an unmutilated chessboard?
A similar problem asks if an ant starting at a corner square of an unmutilated chessboard can visit every square exactly once, and finish at the opposite corner square. Diagonal moves are disallowed; each move must be along a rank or file.
What happens if you remove two black corners on a chessboard?
If the two black corners are removed instead, then 32 white squares and 30 black squares remain, so it is again impossible. A similar problem asks if an ant starting at a corner square of an unmutilated chessboard can visit every square exactly once, and finish at the opposite corner square.
Is it possible to tile an 8×8 chessboard?
One of the most famous of tiling conundrums is the following, a problem which almost every mathematician must have encountered at one time or another. Consider an 8×8 chessboard, where the top-right and bottom-left squares have been removed. Is it possible to tile this mutilated chessboard with 2×1 dominoes?
How many black and white squares are on a chessboard?
However, a quick count reveals that the mutilated chessboard has 30 black squares and 32 white squares. A slicker way to see that there are unequal numbers of black and white squares is to notice that we removed two squares of the same colour from a board that previously had equal numbers of each.
