Great Puzzle! The Three Prisoner Puzzle

My all-time favourite puzzle, that can be solved with logic - no math needed. Sometimes those who are not so good at math, get it quicker.

Category:

Education

Tags:

• puzzle
• math
• logic
• video
• three prisoners
• mathhiker.com

[7x34hj]

Igor knows that his spot must be white. If it were black then both of the other two would have seen one white spot and one black. They both know that there are only two black spots in total (from five) so that means that if one of them had a black spot then one of the other two would be able to see two black spots and therefore claim his spot to be white. Since neither make this claim Igor knows that the other two must be seeing a white spot on his back (and on the other).

[minkusbc]

@7x34hj You nailed it!  Superb logic.

[alfaxen1]

no offence but you have to be really poor in logic to not figure it out in like 2 min without hints ...

[minkusbc]

@alfaxen1 Great for you! But what is the answer and what is your logic?

[ericsosna]

Igor sees white white. He concludes he has white. Qwerty sees white white also. Why couldn't he have reached the same conclusion? Or uiop, who also saw white white?

[minkusbc]

I think people are getting hung up on my phrase "they had equal intelligence". That does not mean that they are EXACTLY equal, they are "of similar" intelligence. However, even if their IQ's were all the same, it is possible for one of them to get a problem that the others do not, (at least right away).

[scotland7yard]

great puzzle!

although there is a second and much darker solution to this puzzle that is not very well known

[gravi1ty]

nah, you're wrong, try again.

[gravi1ty]

@minkusbc this problem doesn't work, because in the end logically you end up with two possibilities: qwerty saw 1 black, 1 white, uiop saw 1 black, 1 white. In this case Igor could be black and both qwerty and uiop would have no way of knowing what they were wearing. Similarly Qwerty and Uiop could have both seen white, and again wouldn't be sure what was on their own backs, therefore IGOR can't make an assumption.

[monkeyboyzinaction]

thank you! this puzzle has been driving me crazy for ages!!! :D

[kiranrajkeralaboy]

@minkusbc

1)Cannot apply in real life

2)Igor was more intelligent

3)Even if they were equal ,they didn't know that

4) Suppose Qwerty thinks if I had white and Igor saw it and he knew Uiop was white he would have figured out that he is white and gone so I must be black but then again if i was black and igor saw it he would have won knowing uiop is still here.So this again leaves a perfect doubt.

the stewardess used empathy not logic.reply please.

[7x34hj]

@TasteForDisaster Yes, but we are 'given' that Igor sees two white spots. If he (or any of them) saw one white spot and one black, then (as you imply), the same logic applies. Perhaps the puzzle would be better if we are given the spots on all three prisoners as: 1(W), 2(W), 3(B); we then have to work out which of them correctly asserts his spot colour, and how he knew this. Regards.

[TasteForDisaster]

@7x34hj but he see's 2 white marks. it would work like you said if igor saw a white and black disk.

[iiCandyx]

Dear minkusbc,

I need to do a project for Math with the subject: Antikythera mechanism. I was wondering if you could help me/ know a person who could help me with this project. The information on the internet isn't kind of enough for my research. I've watched many video's of you and thought maybe you could help me with my project. You're very inspiring and you make math fun btw :)

[7x34hj]

@minkusbc Much gratitude, sir.

[alfaxen1]

@minkusbc has been answerd so many times its no use in me writing it 2.. it be like spaming xD