## Some Chessboard Problems

1. 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.)
2. 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.)
3. 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?
4. 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.)
5. Repeat problem 4, with the added restriction that the two pieces be identical (through rotation.)
Source: Original.
Solution
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