Knight's TourMath brain teasers require computations to solve.
One day, a knight went to the legendary kingdom named Breadland. The Breadlanders love eating bread. They also play chess. What's different from normal chess is that the chessboard they use is 9x7, each player has a queen on each side of the king, one is next to the king and the other is between a bishop and a knight. Also, each side has one more pawn, so that there are totally 4 queens and 18 pawns on the chessboard. In fact, Breadland is a chessboard itself, and is of course 9x7.
The knight was on a square of Breadland, he wanted to visit each square of Breadland exactly once, and return to the square he was originally on. Each step, the knight moved to one of the squares nearest to that on which it stands but the queen can't reach.
Could the knight achieve his goal?
AnswerColor the chess board alternatively black and white, and suppose the lower left corner is black, as in normal chess. Then each move of the knight brought him from a black square to a white one, or vice versa. If he could achieve his goal, there must have been as many black squares as white ones. However, there were 32 black squares and 31 white squares. Hence, the knight could not achieve his goal, and had to repeat some white square.
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