Charlie has 128 identical-looking gold-colored coins; all are counterfeit except one.

He calls Alice into his office and seats her at a table containing two 8 × 8 boards, with a coin on each of the 128 squares, each coin showing a head or tail as he chooses.

He tells Alice which coin is made of gold. Alice can then turn at most 4 coins upside down, replacing them on their squares, but her inversions must all be on the first row of the left-hand board. She then leaves the room.

Bob enters and is seated in the same position, facing the boards. He may take one of the 128 coins.

Find a strategy that allows Bob to always take the gold coin.

Alice and Bob know the protocol in advance and can plan a strategy, but cannot communicate after Alice enters the room.

(In reply to one possible strategy by armando)

Indeed, if Bob was allowed to know the predisposition of the first row before any of the four coins were flipped, then it may be possible for the proposed strategy. Given that he is not given that predisposition, I do not see how Bob could determine which four coins were flipped or not -- less a predetermined selection of squares that would contain those coins, which then does not allow for the eight-digit binary to be expressed.

Posted by Dej Mar on 2018-03-31 00:11:01