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 re(2): one possible strategy by armando)

Okay. I see now. The high-order bit having a predisposed value lets Alice need but flip at most four coins to represent any value in binary from 0 to 127 (i.e., 1 to 128), or 128 to 255 (again,: 1 to 128).

Posted by Dej Mar on 2018-03-31 07:24:41