Green-eyed dragons puzzle

You visit a remote desert island inhabited by one hundred very friendly dragons, all of whom have green eyes. They haven’t seen a human for many centuries and are very excited about your visit. They show you around their island and tell you all about their dragon way of life (dragons can talk, of course).

They seem to be quite normal, as far as dragons go, but then you find out something rather odd. They have a rule on the island which states that if a dragon ever finds out that he/she has green eyes, then at precisely midnight on the day of this discovery, he/she must relinquish all dragon powers and transform into a long-tailed sparrow. However, there are no mirrors on the island, and they never talk about eye color, so the dragons have been living in blissful ignorance throughout the ages.

Upon your departure, all the dragons get together to see you off, and in a tearful farewell you thank them for being such hospitable dragons. Then you decide to tell them something that they all already know (for each can see the colors of the eyes of the other dragons). You tell them all that at least one of them has green eyes. Then you leave, not thinking of the consequences (if any). Assuming that the dragons are (of course) infallibly logical, what happens?

If something interesting does happen, what exactly is the new information that you gave the dragons?

Monty Hall solution

Players initially have a 2/3 chance of picking a goat. Those who swap always get the opposite of their original choice, so those who swap have 2/3 chance of winning the car. Players who stick have a 1/3 chance of winning the car.  The solution is based on the premise that the host knows which door hides the car and intentionally reveals a goat. If the player selected the door hiding the car (1/3), then both remaining doors hide goats and the host may choose either door at random, and switching doors loses in 1/3. On the other hand, if the player initially selected a door that hides a goat (a 2-in-3 chance), then the host’s choice is no longer at random, as he is forced to show the second goat only, and switching doors wins for sure in 2/3.

The Monty Hall Puzzle

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

Boy/girl hair solution

They both lied.

The child with the black hair is the girl, and the child with the white hair is the boy.

(If only one lied they would both be boys or both be girls)

Boy/girl hair puzzle

A boy and a girl are chatting.

“I am a boy”, said the child with black hair.

“I am a girl”, said the child with white hair.

At least one of them lied. What colour hair does the boy have?

Post Office Burglary solution

Solution: Derek was the culprit.

Looking at Brian’s statement if it was Charles, then Brian was lying in his first statement, which makes the second statement true. Which would mean that it was both Charles and Alan. So it can’t be Charles.

Which means Derek was lying in his first statement, which makes the second statement true. Therefore it can’t be Alan.

So Eric’s second statement must be false, meaning his first statement was true, therefore it was Derek.

Post Office burglary puzzle

After a local Post Office burglary, five suspects were being interviewed.

Below is a summary of their statements.

Police know that each of them told the truth in one of the statements and lied in the other.

From this information can you tell who committed the crime?

Brian said:
It wasn’t Charles
It was Alan

Derek said:
It was Charles
It wasn’t Alan

Charles said:
It was Brian
It wasn’t Eric

Alan said:
It was Eric
It wasn’t Brian

Eric said:
It was Derek
It was Alan

How many triangles solution

The correct answer is 13 triangles – the large outer triangle, plus 9 small inner triangles, plus 3 medium size triangles comprised of 3 triangles each.

Murder mystery solution

Culprit               Weapon           Location
Mrs Red          spanner              kitchen
Dr Purple          rope                     study
Major Yellow     lead piping    library
Miss Beige            gun                   conservatory

Snail racing puzzle solution

# Owner   Wore  Colour
1 Alfred       3     red
2 Alice         2     green
3 Arthur      4     blue
4 Anne         1     yellow