Today's puzzle is a retrospective commemoration of UNESCO's World Logic Day, which took place last week. (The date January 14 is also the day Kurt Gödel died and the day Alfred Tarski was born, a calendar coincidence that unites the preeminent logicians of the 20th century.)
This is a logic puzzle and, as is typical of this genre, it's about a group of clever people wearing colorful hats.
However, despite the quirkiness of the setting, this puzzle is a neat explanation of a mathematical idea with interesting real-world applications. Hold on to your hats, everyone!
cue eye
1. Ten logicians are arranged in a line facing the same direction. Each has a red or green hat on their head. Logicians do not know what color their own heads are, nor do they know the color of the hats of the people behind them in line. Since each logician can only see ahead, he only knows the color of the hat of the person in front of him.
One at a time, each logician says aloud the word “red” or the word “green.” All logicians say one of these words, but no logician says them twice.
Can you think of a strategy that the logicians would have agreed upon before lining up so that at least nine people would say the color word that accurately describes the hat on their head?
There are no mirrors or reflective materials. Your knowledge of the color of your hat is entirely inferred from what you see and what you are told.
2. The settings are the same as before, but the hat now has three colors: red, green, and yellow.
Can you think of a strategy where each logician says one word (red, green, or yellow) and at least nine people say the correct color of their hat?
We'll be back at 5pm UK with the solution and an explanation of how this relates to things in the real world.
Please don't give spoilers. Instead, talk about hats and logicians.
We would like to thank Mr. Deniz Salikaya, coordinator of the Free University of Brussels and the University of Lübeck. world logic day.
Since 2015, I have been posting puzzles here every other Monday. Always looking for great puzzles. If you would like to suggest anything, please email me.
