Coin Toss Guess
24 May 2015
Puzzle

Alice and Bob are playing a game. They are teammates, so they will win or lose together. Before the game starts, they can talk to each other and agree on a strategy.

When the game starts, Alice and Bob go into separate soundproof rooms — they cannot communicate with each other in any way. They each flip a coin and note whether it came up Heads or Tails. (No funny business allowed — it has to be an honest coin flip and they have to tell the truth later about how it came out.) Now Alice writes down a guess as to the result of Bob’s coin flip; and Bob likewise writes down a guess as to Alice’s flip.

If either or both of the written-down guesses turns out to be correct, then Alice and Bob both win as a team. But if both written-down guesses are wrong, then they both lose.

Can you think of a strategy Alice and Bob can use that is guaranteed to win every time?

Source

Whitehouse.gov published it in a blog article in May 2015.

Solution

Alice writes down whatever her coin turns out to be. Bob writes down the opposite of whatever his coin turns out to be. Explanation: Alice is guessing that the coin tosses turned out to be identical. Bob is guessing that the two coin tosses turned out to be different.