Place thirteen kings on a regular 8 8 chess board Kings are

Place thirteen kings on a regular 8 * 8 chess board. Kings are allowed to be next to each other, unlike usual rules.

Move one king at a time to an adjacent square. Eventually each king returns to its original square after visiting each other square exactly once.

Prove there\'s a time when every king is not in its original square.

Solution

8*8 Chess board has total 64 squares.

Now assume we have total 26 kings instead of given situation.

Place all the 26 kings on chess board in the pair of 2. (in adjacent squares)

Now remove any one of the kings from these thirteen pairs and replace them with rest of thirteen kings available on board.

It proves that these remaining thirteen kings were initially on thirteen squares and now after replacing them at the same time they are not on those thirteen squares.

which proves that there will be a time when every king is not on its original square.