I was given a puzzle to solve which goes as:- Can a knight start at square a1 of a chessboard, and go to square h8, visiting each of the remaining squares once on the way ?
I reasoned that this won't be possible because both the squares a1 and h8 have the same colour ( say, black ). If we are not considering these squares, then the remaining chess board has 62 squares which means that there are 30 black squares and 32 white squares. If the knight was to visit each of these squares exactly once, then this would mean that we would be having the sequence WBWBWBWB…..W where the pair "WB" would be occuring 31 times. However, this is not possible as there are two extra whites than black. When I submitted this solution, I was told that it is wrong but no explanation was given. Can you help me out?
Best Answer
There may a simpler explanation: to visit all the squares without returning to any takes 63 steps, an odd number, but each step changes the colour, so you cannot finish on the same colour as you started.
Perhaps you were failed because you gave a correct answer which was different to the one the tester was looking for.