## Some Chessboard Problems

- What is the smallest number of moves needed by a chess rook to visit every
square on a chessboard? (A rook can only move horizontally. A "move" can be any length in a single
direction.)
- What is the smallest number of moves needed by a chess queen to visit
every square on a chessboard? (A queen can move both horizontally and
diagonally.)
- A chess bishop can only move diagonally. What is the maximum number
of squares a chess bishop can visit, if it is only allowed to visit each
square once?
- Cut a chessboard into two pieces along the grid lines, then rearrange
the two pieces (with rotation possibly, but not reflection) to try to
achieve the largest number of same-color neighboring squares. (For
example, if you cut off one column, and rotate it, then there will be eight
pairs of adjacent squares of the same color.)
- Repeat problem 4, with the added restriction that the two pieces be
identical (through rotation.)

Source: Original.

Solution

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