Welcome back to Monday! Today's problem is copied from the White House!

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?

## Comments:

Anonymous - 8 years ago

They each write the result of their own flip.

reply permalink

Anonymous - 8 years ago

One agrees to write heads and the other agrees to write tails.

reply permalink

Anonymous - 8 years ago

Alice writes down the result of her flip. Bob writes down the opposite of his flip. If the two flips are the same, then Alice guesses correctly. If they are different, then Bob guesses correctly.

reply permalink

baidarkajoe - 8 years ago

Beautiful! There are two different states. Either the flips are different, or they're the same. This strategy bets on that fact, and comes out a 100% winner!

reply permalink