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 The second part by Brian Smith)

That's quite impressive.

In added explanation: at what would be the end of the game in nim, when each of the gaps between pair members is reduced to zero, this game is not over quite yet, as there are still gaps between one pair and the next.  But each move by your opponent then just creates a new gap within pairs that you can then close immediately.

Posted by Charlie on 2004-04-27 09:50:26