There are 2012 lamps arranged on a table. Two persons Diana and Ethan play the following game.
In each move the player flips the switch of one lamp, but he or she must never get back an arrangement of the lit lamps that has already been on the table. A player who cannot move loses.

Diana makes the first move, followed by Ethan. Who has a winning strategy?

(In reply to re: Possible solution by Ady TZIDON)

Assume d simply selects the same switch each turn - on, off, on, off,..

e can never select d's switch since that would cause a repetition immediately.

We know d wins eventually if all combinations are run through, so the best e can hope for is to run through them all. He can never 'trap' d because d only ever touches one switch, which e can never select, and e is obliged to find a fresh combination every turn.

This is enough to ensure that all combinations are reached, if both players adopt optimum strategies.

Edited on April 18, 2015, 4:52 am

Posted by broll on 2015-04-18 04:48:58