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)
I don't see it so clearly -- in Nim, you take away from a pile, and the other piles stay the same. Here, when a person goes to a lower step, one difference becomes lower but other gets higher.