What's your favorite Enigma / Riddle / Sentence Puzzle?
What's your favorite Enigma / Riddle / Sentence Puzzle?
Tomorrow is a big event at my university. I'd like to make a fun thing where the people of the Board Game society I am in can try to find me for a riddle, kind of a Where is Waldo in a place where there is a crap tone of people to find the NPC that'll give them a Riddle (Maybe something to win? No idea how I could do that detail)
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This one is kinda hard to describe, so I'm including an image. Four people are standing in a row and all are looking to the right (EDIT: On the image, the fourthperson is looking left. That doesn't matter, because nobody can see through the wall). First and third person have blue hat, second and fourth have red hat. There's a wall between third and fourth person. Nobody knows what color is their hat. Everybody can only see hats of people on their right side (left/right sides are from the perspective of us, seeing them from the side). Nobody can see through the wall. For example first person can see the second and the third person. The second can only see the third person. They know that two of them have red hat and two of them have blue hat. They are told that if anybody says aloud the color of their hat, they are free to go. (They are captives or something). If anybody says the wrong color, they are all gonna be killed. They can't obviously turn around, talk to each other or something like that. They can't guess. Are any of them going to tell his hat's color?
Let's number the dudes in your image form left to right: 1, 2, 3 and 4.
Dudes 3 and 4 have no useful information. They stay silent.
Dude 1 can see one of each hat colour on the dudes in front, but cannot determine their own colour without knowing the hat colour of dude 4. They stay silent.
Dude 2 can see the hat colour of dude 3. They can determine that either they themself or the dude behind must have a different hat colour. The dude behind - dude 1 - can see both of the hat colours in front, but stays silent. This lets dude 2 know that they and dude 3 must be different colours (otherwise dude 1 would have known their own hat colour).
Therefore, dude 2 knows their own hat colour must be different to the dude in front and announces the colour of their own hat.
That's correct!