Earlier today I set you the following puzzle:
You and a friend have been captured on a desert island ruled by a crazed mathematical despot. You will be locked in separate cells in the island’s prison, and then set the following task:
Every minute for an hour you will each flip a coin. The flips are simultaneous, and after each flip you will make a prediction as to whether the other person’s flip was heads or tails.
So, you both make 60 flips and 60 predictions.
The despot rules that he will kill the two of you if on any one of the 60 predictions you are both correct. (In other words, you both flip, both predict the result of the other person’s flip, and are both right). To escape with your lives at least one of you must predict wrongly each time.
You are given ten minutes to think up a survival strategy before being taken to the cells. Once you are in the cells you cannot communicate with each other, although you are obviously able to see the results of your own flips.
Can you guarantee your survival, and if so, how?
Solution
This puzzle seems difficult at first, requiring some kind of trick or extra clever strategy, but the solution is simple.
You will survive if you use the outcome of your coin flip as your prediction, and your friend uses the opposite of their coin flip as their prediction. (Or vice versa).
So, if you flip heads, you predict heads. If your friend flips heads, they predict tails.
Here’s the full table:
You flip H, friend flips H. So you call H, friend calls T. Only one correct prediction.
You flip H, friend flips T. So you call H, friend calls H. Only one correct prediction.
You flip T, friend flips H. So you call T, friend calls T. Only one correct prediction.
You flip T, friend flips T. So you call T, friend calls H. Only one correct prediction.
You might not have thought that the table would work out so neatly, but when you go through the options you will find that it does. Evil despot outfoxed!
Since this strategy always results in one correct prediction, the question could have been phrased with that requirement, as one reader noted:
@alexbellos nice puzzle. the solution also works in reverse i.e. the despot insists the at least 1 person gets it correct
— Conan Farrell (@Con_Far) August 1, 2016
Of the lateral-thinking answers, I liked this one best:
@alexbellos if the coins aren't fair, then yes, if they are fair then predict edge and you should be fine
— James Clare (@bluecombats) August 1, 2016
Since coins have a 1 in 6000 chance of landing on their edge on a flat surface, according to science....
Hope you enjoyed the puzzle, I’ll be back in two weeks.
I post a puzzle here on a Monday every two weeks. If you want to propose a puzzle for this column, please email me I’d love to hear it.
I’m also the author of three popular maths books including Alex’s Adventures in Numberland and the maths colouring book Snowflake Seashell Star. You can check me out on Twitter, Facebook, Google+, my personal website or my Guardian maths blog.
