Logic: Does My Head Look Big In This?

I think this is worth 150 credits for the first correct answer.


This is a true story...apparently. A friend of a friend knows the people involved, so it must be true. ;-)

Tom, Dick and Harriet were trekking through the jungle in South America. Accidentally they strayed into the Holy Lands of the ancient Bungee Tribe.

Traditionally, the penalty for this had been instant death.

However, back in the 60s a new wave of liberals had got into power and many of the old punishements had been banned. The punishment for this offence had been replaced by Spiritual Cleansing. The guilty parties were not sentenced to death, but had to live the life of a monk in the monastrey fro a year and a day. Rations were simple but adequate. TV, and all modern comforts are banned. The waking day (which starts at 5 am) is divided between reading ancient philosophy and toiling in the fields.

Recently, however, there has been a bit of a backlash, with hardliners calling for a return to stricter punishments. Moreover, the availability of cheap air-travel has led to the monastries becoming overcrowded with Brit, Aussie and Kiwi back-packers.

A compromise has now been found, as was explained to Tom, Dick and Harriet.

They will be given a challenge. If they pass, they are released and escorted to the borders of the Holy Land and bade farewell.

If they do not accept the challenge, they will spend a year and a day in the monastrey.

If they do accept the challenge, but fail, they will be smothered in fishbait and dipped slowly (feet first) into the local Piranha filled river.

The Elders have been watching Who Wants To Be A Millionaire on Satellite TV, and have realised it is more fun to let the contestatnts see what the challenge will be before they have to decide to accept or not.

Tom, Dick and Harriet know each other quite well. They each know the others would rather avoid the monastrey if possible. But none of them would want to gamble. In other words, if they see the challenge and are completely sure then they should go for it. Otherwise, they should pass. Each of them knows the other 2 are clever, logical, calm in a crisis and good at puzzles.

After being allowed a quick chance to confer with the others, Tom, Dick and Harriet are told they must not speak to each other or communicate in any other way again until the challenge is over, or else they will get the death penalty.

They are shown a chest. Inside are 5 head-dresses. 3 have blue feathers, and 2 are red.

They are told that each of them will be allocated one of the head-dresses from the chest. They will each be given one and only one (there will be no swapping). The challenge will be that they have to guess what colour head-dress they have on. There is no way of telling by smell etc and there is no chance of seeing your own reflection or catching a glimpse out the corner of your eye, etc.

If any of one of them guesses correctly. They all go free. If any one of them guesses incorrectly they all die. If all pass rather than guess, they all get the monk treatment.

They are each then blindfolded and the headgear is put on them. They are tied to chairs in a triangle and the chest is in the middle. Naturally it is closed and there is no chance of seeing inside to see which 2 head-dresses are left inside.

Tom is first up. His blindfold is removed and he can see what Dick and Harriet are wearing.

The Chief tells him he has one hour to make his decision. At the end of the hour, he announces, "Sorry, I pass. I do not know what colour headgear I have".

Tom's headgear is removed and put back in the chest. Tom is gagged and blindfolded again and reminded not to try to communicate with the others (which he obeys).

Dick then has his blindfold removed and can only see what Harriet has on. Once again, at the end of the hour he says he does not know his own colour. His head-dress is also removed and put back in the chest. He is gagged and blindfolded again and reminded not to try to communicate with the others. He also obeys.

Finally, it is Harriet's turn. The Chief prepares to start the solemn ritual of taking off the blindfold and giving her one hour to decide. "Nah, don't bother!" says Harriet. "I know my colour. It is ...................Now untie me and point us to the nearest Starbucks."

She was right. So what colour did she say, and how did she know?

[nareluin]

She said "Blue"... And this is what I think:

Inside are 5 head-dresses. 3 have blue feathers, and 2 are red

Originally Posted by Padzok

Tom is first up. His blindfold is removed and he can see what Dick and Harriet are wearing

Harriet must have thought:

"If Tom had seen 2 red head-dresses he would have been certain he had a blue one on (She knew he was smart enough to figure this out). But he passed, so, chances are that he either saw two blue head-dresses, or a blue one and a red one.

If Dick had seen a red head-dress on me (Taking into account the possibilities left by Tom's answer) he would have known his head-dress was blue. But he passed too..."

So Harriet figured out that her head-dress had to be blue.

nareluin is correct


& very quick too

150 points on their way. Spend them wisely.

[Benny]

Naurelin posted their answer while I was still writing mine. Damn! I agree, anyway.

My answer was similar but went something like this:

Tom (T), Dick (D) and Harriet (H) with Blue (B) and Red (R) feathers...

If T saw R and R then they should know they were B. They didn't so the possibilities are:

  T  |  D  |  H
-----+-----+-----
 R/B |  R  |  B
 R/B |  B  |  R
 R/B |  B  |  B

If D saw R on H then they should know that they were B (otherwise they were R and T would have seen R and R). They didn't so that means that the possibilities are:

  T  |  D  |  H
-----+-----+-----
 R/B |  R  |  B
 R/B |  B  |  B

or more simply

  T  |  D  |  H
-----+-----+-----
 R/B | R/B |  B

Therefore H must be B!

Benny's answer is also correct.

Harriet probably was very thorough in thinking through all the possibilities. She had a full hour while Dick was thinking to realise that either Dick should get it and it would never reach her, or else she must have Blue.