Questions tagged [hat-guessing]
Cooperative games where a team of players must try to guess the color of their hat, but can only see their teammates' hats.
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Infinitely many hats
We are given countably many people numbered $1,2,3,\ldots$ for all $n\in \mathbb{N}$, each wearing a hat that is either black or white. No-one can see the color of their hat, but everyone can see ...
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8 Prisoners wearing hats
A warden lines up these prisoners. He announces, "I see a white hat." He then leaves the room. Every few minutes he comes back in and asks if anybody knows their hat color. Anyone who figured it out ...
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Guess simultaneously, color of your hat, no passing allowed
1000 logicians standing in a circle are blindfolded and a hat of either black or white color is placed on each person's head. The blindfolds are then removed and each person can now see everybody's ...
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Hat Puzzle with 5 different colours and 3 people
A dad wants to play a game with his 3 children this Christmas. He has a bag with 5 hats; 1 white, 1 yellow, 1 red, 1 blue and 1 black in it. The hats are all equal except their colour. He will place ...
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Again! 6 prisoners, 2 colors, one mute
After that last game, the warden didn't like that they escaped. So he made them all play again. Like before, they know there are 6 prisoners, 3 red hats and 3 white hats. They know one prisoner is ...
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6 prisoners, 2 colors, one mute
Just like the classic 4 prisoners hats riddle, here we have 6 prisoners buried to their necks in the ground. They can only look straight ahead so that A only sees B, C, D, E while B sees C, D, E, and ...
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Number hats puzzling [duplicate]
10 people will stand in a circle, and each have a hat placed on their head. The hats will each be labeled with a digit between 0 and 9, with repeats allowed. They will be able to see everyone's hat ...
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3 Numbers on Hats, A = B + C
This feels like it should be a common puzzle, but I haven't found anything exactly like it searching online, so here goes. Apologies if it's a duplicate.
Three logicians, person 1, 2, and 3, along ...
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10 prisoners and 10 lists of numbers [duplicate]
10 prisoners are held captive by a cruel warden. One day he gathers them in the prison hall and tells them about a new game he wants to play:
"Tomorrow, I will assign each one of you a random ...
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MORE Prisoner Hats!
The king arrests all married couples where both spouses are PhDs in Math, Computer Science, or Logic. He holds each couple separate from the others and tells each couple in turn that all the rounded-...
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Numbered hats, Warden and Maths
You are one of 4 prisoners. Tomorrow will be a deciding day: the warden has told you and your cellmates that you can all go free, or all be executed, depending on how you answer tomorrow's challenge. ...
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Guessing hat colors. 4 prisoners
This is a variant about guessing hat colors. You may want to try
Hats and alien or Guessing hat colors or Four prisoners wearing black and white hats.
Statement
4 prisoners are to be executed. The ...
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Hat puzzle - 7 prisoners
There are 7 prisoners buried up to their necks in sand. 6 are on one side of a wall, all facing the wall. They are lined up such that the furthest from the wall can see the 5 prisoners closest to the ...
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Guessing game with infinity coin flips
Evan and Ollie are going to play a game as a team. The two friends placed in separate rooms, and then a coin is flipped infinitely many times*. Evan is told the results of the even numbered flips, ...
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Five Hats and Three Logicians
Three logicians were seated around a table. They were blindfolded and a colored hat was placed on each of their heads. They were told a true statement
The hats on your heads were chosen among 3 ...
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