There are 15 stairs arranged in a line. There are 6 people on various different steps.

The only rule is you can only move a person if you move it to any lower vacant stair.

In a two player game, you alternate moving single people. The last one to move a person wins! What strategy should you use in order to win?

What strategy would be used if the people couldn't pass each other when moving down the stairs?

(In reply to re: The second part by Federico Kereki)

It will be the opponent, not knowing the nim connection, who might place a person who is the lower member of a pair on a lower step (remember only the gap between the topmost and second topmost, the gap between the third topmost and the fourth topmost, etc. count), thereby actually increasing one of the nim totals (it does not decrease another when this happens as that gap doesn't count).  Whenever this happens, you, the player who knows the nim connection, can just restore the gap between the higher person in the pair and that lower person the opponent had moved, and the nim totals are back to where they were before the opponent's move.

If the opponent had indeed moved a top player of a given pair (i.e., 1st, 3rd, 5th, etc. person from the top), then that move was just an ordinary nim move, as again, the gap from the 2nd to the 3rd or 4th to 5th, etc. does not count.

This is similar in nature to the end-game that I had mentioned in a previous posting in response to Brian Smith, that extends the end a bit beyond that of the traditional nim game.

Posted by Charlie on 2004-04-27 20:50:12