Problem of the Week 1245
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
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.
As usual, Alice and Bob know the protocol in advance and can plan a strategy, but cannot communicate after Alice enters the room.
Note: If Alice could invert up to 7 coins, then she could arrange the first 7 squares of the left-board's first row to be any of
Source: Peter Saltzman, Jim Tilley, and Stan Wagon. ("Goldilocs" abbreviates "Gold Locations.")