Question

Arthur and Merlin enter a gambling contest. The contest has 1000 rounds. For each round, Arthur and Merlin write independent predictions for a coin toss. After the coin is tossed their predictions are revealed and if both are correct their team scores a point. If either ever speaks or writes anything other than H or T for a prediction their team is disqualified.

Arthur and Merlin realize that Merlin will be able to use his magic to know the results of all coin tosses in advance but he will not be able to communicate this information to Arthur other than by using a code formed from his guesses as H and T.

For partial credit, explain a strategy by which Arthur and Merlin can expect to score a point in more than 600 of the rounds. Full credit will be given for strategies that succeed in more than 650 rounds.

Answer 1