Logic Puzzle

[Felipe dos]

I've just returned from my new Theory of Knowledge class, which is basically the coolest class anyone like me could ask for. It's just one big philosophical discussion.

In this class we were taught a very unique problem that requires some serious brains, but is entirely solvable.

One man sits next to another on an airplane. They strike up a conversation and the first man eventually tells the second that he (the first man) is the father of three sons. The second man asks what their ages are. The father challenges him to guess.

The father gives the man a clue in that the ages of the three sons multiplied together create a product of 72.

A x B x C = 72.

The man says he cannot possibly know the correct answer with the given information, which is true. The father therefore tells him that the sum of the ages of the three sons is the same as their flight number.

A + B + C = #

The man replies again with the fact that he cannot know the answer without simply guessing. The father gives him one final clue through stating that the name of his youngest son is David.

Youngest son = David.

The man therefore knows the exact age of each of the individual sons.

What are the ages of the three sons?

This question is entirely possible to answer with the given information. It is not a trick in any form. There is neither a play on words nor a single statement meant to be misleading. You do not need to know the number of their flight or the age of David, only that he is the youngest of the three.

I will worship anyone who answers this correctly. If you give up, PM me for the answer.

Debo37, WeaselJOE37, and Muskrat01 are all forbidden from answering, as they go to my school.

[Shock Theta]

• A x B x C = 72
  • There are twelve possible solutions.
• A + B + C = X
  • There are two possible solutions. The second man knows his flight number, and cannot answer the question. Thus, as there are only two cases of the sum of the age of each of the three children giving the same result - 14 - this is both the flight number and the two possible age sets.
• One child is younger than the other two.
  • There is one possible solution.

I assumed the ages had to be whole numbers, otherwise this is unsolvable.

I'll take sterling. Thanks.

[Thorax tehGREAT]

I have to agree with Shock on this. I figured it out after reading it a couple of times.

[CaMOfo]

I PMed you. I think I solved it.

[SargeantSarcasm]

Originally Posted by Shock Theta

• A x B x C = 72
  • There are twelve possible solutions.
• A + B + C = X
  • There are two possible solutions. The second man knows his flight number, and cannot answer the question. Thus, as there are only two cases of the sum of the age of each of the three children giving the same result - 14 - this is both the flight number and the two possible age sets.
• One child is younger than the other two.
  • There is one possible solution.

I assumed the ages had to be whole numbers, otherwise this is unsolvable.

I'll take sterling. Thanks.

Yeah, that was the exact approach I was taking, except I got caught up in the whole situation I'm sure you've seen.. so I couldn't get to the math detailing part you did in excel...sadfaic...

this is as far as I had written:

Originally Posted by SargeantSarcasm

The factors of 72 are as follows: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

So. If he said that they are multiplying the ages of the sons, and that equals 72, then the youngest, David, cannot be 0 years old, or still in the womb. Which was proven above thereby voiding this entire statement, its just to get it out of my head.

Woe is me.

[Felipe dos]

Looks like Shock's got it.

How about the general satisfaction of knowing what very few people do as a reward?

[What's A Scope?]

Originally Posted by Felipe dos

Looks like Shock's got it.

How about the general satisfaction of knowing what very few people do as a reward?

How does the David part help?

[hArIkIrI]

ooh i heard this riddle before, its because david tells you there's a younger son.

[Felipe dos]

Yes. Using the method Shock did, you find that there are two possible answers. One is 8, 3, and 3, the other is 6, 6, and 2. Only the second has one youngest child, therefore it must be the correct answer.

[What's A Scope?]

Originally Posted by Felipe dos

Yes. Using the method Shock did, you find that there are two possible answers. One is 8, 3, and 3, the other is 6, 6, and 2. Only the second has one youngest child, therefore it must be the correct answer.

How do you know it has to equal 14?