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# Red-Eyed Dragons

100 dragons live on an island. They have a strange tradition: any dragon who knows their eye color must leave the island at midnight. Because of this rule, the dragons never talk about eye color, though they can see everyone's eye color except their own (there are no mirrors etc. on the island). They also know that every dragon has either red or blue eyes.

This quiz deals with problems involving this general scenario. The main point is that inaction can still give knowledge. In particular, if a dragon does not leave the island at midnight, all the dragons know that the dragon doesn't know their own eye color.

Recall that there are 100 dragons on the island, and they leave at midnight if they know their own eye color (which is either red or blue).

Suppose the traveler--not knowing of the dragons' custom--says, "Wow, half of you have red eyes, and half of you have blue eyes!" Which of the following will happen to the dragons?

Recall that there are 100 dragons on the island, and they leave at midnight if they know their own eye color (which is either red or blue). In reality, all the dragons have red eyes.

Suppose the traveler--not knowing of the dragons' custom--says, "I've seen 99 of you, and I haven't seen any blue eyes yet!" Which of the following will happen to the dragons?

(Note that you can assume anything the traveler says is conveyed to all dragons on the island, even the one the traveler has not seen. Also, it is not clear from the dragon's perspective who the traveler has seen and not seen.)

The previous problem demonstrates how the traveller can give information even when it looks like he isn't: even though the dragons already know there are at least 99 dragons with red eyes (since they can see every other dragon), they don't know that every other dragon knows this until the traveller says so.

Recall that there are 100 dragons on the island, and they leave at midnight if they know their own eye color (which is either red or blue).

Suppose the traveller says (to no dragon in particular), "I've never seen such beautiful red eyes!" That night, one of the dragons leaves the island. What happens to the other 99 dragons?

Let's consider a simpler case where there are only two dragons on the island. As before, they leave at midnight if they know their own eye color, which is either red or blue. Again as before, a traveller appears and says, "I've never seen such beautiful red eyes!"

In reality both dragons have red eyes. What happens to the dragons?

Now suppose there are three dragons on the island, each of which leaves at midnight if they know their eye color (which is either red or blue). The traveller again says, "I've never seen such beautiful red eyes!"

In reality all dragons have red eyes. What happens to the dragons?

Now the main problem: there are 100 red-eyed dragons on the island, and they leave at midnight if they know their own eye color (which is either red or blue). The traveller says, "I've never seen such beautiful red eyes!"

In reality all dragons have red eyes. What happens to the dragons?

Recall that there are 100 dragons on the island, and they leave at midnight if they know their own eye color (which is either red or blue). In reality, all the dragons have red eyes.

Suppose the traveller--not knowing of the dragons' custom--says, "I've never seen such beautiful red eyes!". However, one of the dragons doesn't hear the traveler (the other 99 dragons are also aware the 1 dragon didn't get the information, nor is the dragon conveyed the information). What happens to the dragons?

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