# Questions tagged [blue-eyes]

For questions related to the puzzle of islanders who can only leave when they deduce the colour of their own eyes.

15 questions
Filter by
Sorted by
Tagged with
72k views

### In the 100 blue eyes problem - why is the oracle necessary?

The riddle Randall Munroe (of xkcd fame) has, a bit hidden on his site, a logic puzzle: A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a ...
3k views

### The origin of the blue eyes puzzle

The Blue Eyes puzzle is possibly the most popular induction-based puzzle known. Is it really known who was the first to come up with it (in any form). The link at xkcd says: I didn't come up with ...
680 views

### Numbered Logicians near the Blue Eyes island

There is an island near the famous Blue Eyes island where 100 perfect logicians live, each with a number between 1 and 100 (repetitions allowed) tattooed on their forehead. They know all the numbers ...
628 views

### Exponential time in a Blue Eyes variant

I created a variant of the Blue Eyes problem where the logic took 4901 days (over 13 years) to totally play out. I thought this was nice, but I was hoping for an even longer period of time. Of ...
888 views

### Mixed Up Memberships

In a small town, there exist a number of organizations of people. Each year, they send out a list of their members to everyone and this is the official way in which people know they are part of an ...
2k views

### The Dot-town suicide

Each resident of Dot-town carries a red or blue dot on his (or her) forehead, but if he ever figures out what color it is he kills himself. Each day the residents gather; one day a stranger comes and ...
729 views

### Variants to blue eyes puzzle

Here are some variants to the Blue Eyes puzzle. All the rules are the same, but there are differences in (a) the number of people of different eye colors and (b) the oracle's statement. It is not ...
2k views

### In the blue-eyes puzzle, why can't they skip ahead? [duplicate]

In the solution to the Blue Eyes logic puzzle, there is a follow-up question: Each person knows, from the beginning, that there are no less than 99 blue-eyed people on the island. How, then, is ...
837 views

### Green Eyed Oracle Variant - Not a Multiple of $17$

$100$ perfect logicians have been gathered on an island. It is common knowledge that logicians always have blue or brown eyes, though on this island, all eyes are blue. However, there are no ...
529 views

### Another twist on the blue-eyed puzzle

In Variants to blue eyes puzzle we explored what would have happened if the oracle of the Blue Eyes puzzle had said something different with different numbers of islanders. I've got another one for ...
923 views

### A false and a true statement in the blue-eyed puzzle

Here is a variant on the blue-eyed puzzle. I hope it brings at least some more difficulty than the original one, even if you know the solution to the original. The Guru makes the following statement:...
434 views

### Variant to blue eyes puzzle - selfish logicians

This is a variation of the blue eyes puzzle. Suppose the logicians want to get off the island. They are selfish and think only of themselves. They may help others as well, but solely for their own ...
134 views

### Mensa 3rd Grade Recess Game [closed]

Mensa 3rd Graders At Recess There are dozens of variations of this puzzle type, but I put my own spin and characteristics to it. It is lunch time for the little ones at Mensa Mini's Private School. ...