Question 152
The 64 cells of an $8 \times 8$ chessboard have 64 different colours. A Knight stays in one cell. In each move, the Knight jumps from one cell to another cell (the 2 cells on the diagonal of a $2 \times 3$ board); also the colours of the 2 cells interchange. In the end, the Knight goes to a cell having a common side with the cell it stayed at first. Can it happen that there are exactly 3 cells having colours different from the original colours?