Princeton professor Ed Felten joined the staff of the White House as Deputy US Chief Technology Officer last week.
The brainteaser is as follows:
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.
The puzzle is this: Can you think of a strategy Alice and Bob can use that is guaranteed to win every time?
To get you started, here is an example of a strategy that doesn’t work: Alice and Bob decide in advance that they will both guess heads. This isn’t a guaranteed-winning strategy, because a quarter of the time they will both flip tails so both guesses will be wrong. They’ll win 75pc of the time, but that isn’t enough – they need to win every time.
Felten tweeted out a clue for the brainteaser on Monday and says he will reveal the answer in a future blog post.
Brainteaser hint: Alice is wrong 50% of the time; Bob is right 50pc. Bob must be right exactly when Alice is wrong. https://t.co/tAFPtSaQkQ
— Ed Felten (@EdFelten44) May 18, 2015
Before joining the staff of the US president, Felten served as the Robert E. Kahn Professor of Computer Science and Public Affairs at Princeton University, where he was also the founding Director of the Center for Information Technology Policy. He also served as the first Chief Technologist at the US Federal Trade Commission, and worked with the US Department of Justice Antitrust Division.
So he’s a prettty smart guy – but can you solve his brainteaser?
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