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(2): Possible solution
Your first post is confusing and I don't understand it.
The reply [re(2)] makes perfect sense.
Whoever goes first is guaranteed an unused combination as long as they only ever flip the same switch every time.
Can a cutoff exist so that the game doesn't use all 2^n moves? Even if such a cutoff does exist the outcome is the same, the second player just loses sooner.
Posted by Jer
on 2015-04-18 22:18:40