The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

Antrax · ESL Student

I was actually a bit surprised that I haven't heard of this one until recently, it seems like a natural extension of the many other hat puzzles (one I asked about a while ago, in particular).
So, 10 people, 10 hats. Each hat has a single digit on it, digits can occur more than once. Let people confer, place hats on heads, every person guesses what digit the hat on his head bears without hearing other guesses and if at least one of them guesses correctly, profit.
What's the winning strategy?
_________________
After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!

ralphmerridew · Daedalian Member

Thought I mentioned this as a generalization:

Beforehand, each person picks a different digit from 0 to 9. After they receive the hats, each assumes that digit is the last digit of the sum of all hats, and calculates what number is on his/her hat under that assumption. Exactly one of them will be right.

Antrax · ESL Student

Yeah, that's what I had as well. I thought it was cute, especially because I got to it from a much more complicated "iterative guessing" algorithm.
_________________
After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!