What’s the similarity between a logic puzzle and an apple? Deduce! Sorry … let’s begin.
You and your two friends Pip and Blossom are captured by an evil gang of logicians. In order to gain your freedom, the gang’s chief, Kurt, sets you this fearsome challenge.
The three of you are put in adjacent cells. In each cell is a quantity of apples. Each of you can count the number of apples in your own cell, but not in anyone else’s. You are told that each cell has at least one apple, and at most nine apples, and no two cells have the same number of apples.
The rules of the challenge are as follows: The three of you will ask Kurt a single question each, which he will answer truthfully ‘Yes’ or ‘No’. Every one hears the questions and the answers. He will free you only if one of you tells him the total number of apples in all the cells.
Pip: Is the total an even number?
Blossom: Is the total a prime number?
You have five apples in your cell. What question will you ask?
I like this puzzle because it is a clever combination of two classic types of logic problem, so-called “common knowledge” problems where the protagonists have both private and public information, and truth-telling problems where you must devise a question that gets you the desired outcome from a “Yes” or a “No”.
For those of you who have forgotten what prime numbers are, they are the numbers that are divisible only by themselves and 1. The sequence of prime numbers starts 2, 3, 5, 7, 11, 13, 17, 19, 23,…
We can also assume that you and your friends are all perfect logicians.
The puzzle is adapted from one by Prem Prakash, an electrical engineer from Bangalore, India, who has taken early retirement to develop puzzle-based teaching workshops, and also as @1to9puzzle posts daily puzzles on Twitter.
I’ll be back at 5pm GMT with the solution. Meanwhile, NO SPOILERS! Toodle PIP!
My latest book Puzzle Ninja: Pit Your Wits against the Japanese Masters, contains more than 200 of the most original, beautiful and interesting puzzles that have been crafted in Japan over the last few years. You don’t need to be a logician to deduce that Puzzle Ninja would make a perfect Christmas gift!
I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.