Fun Logic Problem

[chumdawg]

Three logicians are standing in a circle, facing eachother. Each logician has a positive, unique, integer written on his forehead. One of the numbers is the sum of the other two. And, none of them have any prior knowledge to what their number is.

A man comes up to Logician A and asks, "Do you know what number written on your head?" He answers, "No."

He then approaches Logician B and asks, "Do you know what number written on your head?" He answers, "No."

He then approaches Logician C and asks, "Do you know what number written on your head?" He answers, "Yes, it's 50."

What numbers do A and B have on their foreheads?

[Ninkobei]

I can think of more than one answer, if Logician C is correct on his estimation, which leads me to believe my answers are wrong. Is there even an answer to this question? the first numbers that come to me are 24 and 26. The second numbers are 20, 70. but there are definitely many more possibilities out there. Could it be a trick question and are the numbers 5 and 0?

[jthig32]

*Edit* If they have to be unique I have no idea. I thought at first it was 25 and 25, which would account of how he knows his is the one the other two add up to.

there must be some trick, there's tons of possiblities if taken at face value.

5 and 0 might actually be the right answer.....

[u2sarajevo]

5 and 0 could not be right because the sum of those numbers is 5, not 50. I think 25 and 25 would make logical sense. A and B would see 25 and 50, so they would not know if their number was 75 or 25. Only C, having 50 on his head seeing 25 and 25 could make that conclusion. The only flaw in that logic is if the number on his head could be 0... A positive integer is any number to the "right" of zero, negative integer is to the "left" of zero.

Add to that you saying they had to be unique.

Argh.

Is it valid, and true that C actually does have 50 on his head? Maybe he came to the wrong conclusion, given that the answer would be "not enough information to determine".

[chumdawg]

U2, you are kinda on the right track, I think. The key to solving this problem is definitely that all three numbers are unique (no duplication, such as having two 25's).

And yes, C is correct and he does have 50 on his head. Assume, also, that all three logicians correctly use perfect logic in answering their questions (in other words, whether they can or cannot know their own number).

EDIT: there is one correct answer.

[u2sarajevo]

Okay, how about A and B have the numbers 20 and 30. The only other possible number C could have had if that's the case is 10. If C had 10, the others could deduce their numbers. But since they said they did not know their numbers C knew he had to have 50?

Is that right? Logically from all three logicians that would hold true.

[chumdawg]

BINGO!!!

Good work. Took me a long time to come around to it.

[mavsman55]

[img]i/expressions/face-icon-small-confused.gif[/img]

confused.

[Caliente]

Secret picture of u2sarajevo....................[img]i/expressions/face-icon-small-wink.gif[/img]

[img]http://rds.yahoo.com/S=96062883/K=pinky+and+the+brain/v=2/SID=w/l=IVS/SIG=122q8qj6r/EXP=1110575784/*-http%3A//www.sg1871loeberitz.de/bilder/brain.jpg[/img]

[jthig32]

Actually, technically only one of the others would have been able to tell what his number was if C had 10, but that is the correct answer. Good job, and thanks, it was driving me nuts.

[u2sarajevo]

Let's reason that out.

A - 30
B - 20
C - 10

A sees 20 and 10, so he knows he is 30 because he can't be 10.
B sees 30 and 10.... hmmm. You are right. B can be either 20 or 40. Sorry bout that.

But the key is that because A and B didn't know their numbers, it left only one possible solution for C.

Pretty cool problem.

[Ninkobei]

Once again, fooled by logic. I need to upgrade my Mr. Spock implant