### Brain Teasers

# Missing Chess Pieces

After reading the postcard from his room mate, who is on a one year world cruise, Mad Ade removed his special gold and diamond encrusted chess set from its secret hiding place (behind the huge pile of empty kebab wrappers), in anticipation of his friend Smelly O'Riley popping round for a game. Imagine Mad Ade's surprise to find all the diamond encrusted gold figures missing, all that is except one solitary Rook. He placed the rook on the chess board and began to think.

If a Rook can move any number of squares sideways/forward, but not diagonally, then what is the minimum number of moves the Rook needs to make, in order to pass over all the squares on the chessboard and return to the original position?

Note: Take any square as a starting position for the Rook.

If a Rook can move any number of squares sideways/forward, but not diagonally, then what is the minimum number of moves the Rook needs to make, in order to pass over all the squares on the chessboard and return to the original position?

Note: Take any square as a starting position for the Rook.

### Answer

16 movesAs a Rook can move any number of squares sideways/forward, but not diagonally, and there are 8 rows and 8 columns on the chessboard; the Rook needs a minimum 16 moves to pass over all the squares and return to the original position.

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## Comments

I think that is the answer, too (and I have a tour that does it), but I don't think the proof is quite that simple. For example, a rook can cover a 2xn chessboard in 4 moves, no matter how big n is. And a 3x3 chessboard seems to require 7 moves.

Sorry kids...the answer is 15! Start at the bottom left. Move up to the top left, 1 move. Over on square to the right, 1 move. Down to the bottom, 1 move. Continue this way to the bottom right. Voila, 15 moves.

OOPS! My apologies, 16 moves it is. I didn't realise we had to end at the starting position.

I stand amazed at this one! A man finds all but one of his diamond encrusted chess pieces missing, and all he can think of is how many moves that solitary piece can make?

a bit vague... perhaps an actual demonstration desciption would help? (not that I need it)

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