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leonard Regular user North Carolina 148 Posts |
This problem might be too simple for many of the readers of this thread. But I have some free time, so here goes.
Two mathematician are walking down a street, when the following conversation ensues: Mathematician 1 (M1): How old are your three children now? Mathematician 2 (M2): The product of their ages is 36. M1 (after some walking): Perhaps another clue would be of help. M2: The sum of their ages is the address on that building across the street. M1 (after further walking): One final clue and I should have the answer. M2: The oldest one likes ice cream. M1: I’ve got it, their ages are __, __, and __. |
Scott Cram Inner circle 2678 Posts |
Let's see. The only possibilities are:
A) 1, 1, 36 (Sum: 38) B) 1, 2, 18 (Sum: 21) C) 1, 3, 12 (Sum: 16) D) 1, 4, 9 (Sum: 14) E) 1, 6, 6 (Sum: 13) F) 2, 2, 9 (Sum: 13) G) 2, 3, 6 (Sum: 11) H) 3, 3, 4 (Sum: 10) We never hear M1 mention a "baby", just children. That eliminates A through E. Now, buildings tend to avoid associations with the number 13 (many won't have the address of "13", or even number a floor as the 13th), so that lets out F. Finally, most parents avoid giving ice cream to pre-schoolers, so that would seem to eliminate H. The only possibility that remains is that the kids are 2, 3, and 6. |
TomasB Inner circle Sweden 1144 Posts |
I think the answer is 2, 2 and 9. The house number must be 13 or otherwise M1 would not need to ask for yet another clue.
/Tomas |
Scott Cram Inner circle 2678 Posts |
If the house number must be 13, then the kids could also be 1, 6 and 6.
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TomasB Inner circle Sweden 1144 Posts |
No, because then there would be no "oldest" kid. He learns in the final clue that there is only one kid that is the oldest.
/Tomas |
leonard Regular user North Carolina 148 Posts |
I agree with Tomas 100%. Now I have to go find a problem I don't know the answer to.
leonard |
Dave Le Fevre Inner circle UK 1666 Posts |
I heard it originally as follows:
A guy is doing a door-to-door survey “Excuse me madam, I'm sorry to bother you, but could I ask whether you have any children?” “Why yes, I have three children” “Could you tell me their ages, please?” “If you multiply their ages together, you get 36” He smiles, and says “Well, that doesn't tell me how old they are” “And if you add their ages together, you get the number of this house” He takes a pace back, looks at the house number, thinks briefly, and says “Well, that still doesn't tell me how old they are” “And the youngest has red hair” “Thank you, madam”, and he writes down their ages and leaves The three ages whose product is 36 must be one of the following sets of numbers 1 1 36 1 2 18 1 3 12 1 4 9 1 6 6 2 2 9 2 3 6 3 3 4 The sums of those sets are as follows 1 + 1 + 36 = 38 1 + 2 + 18 = 21 1 + 3 + 12 = 16 1 + 4 + 9 = 14 1 + 6 + 6 = 13 2 + 2 + 9 = 13 2 + 3 + 6 = 11 3 + 3 + 4 = 10 Therefore the house number must be one of 10 11 13 14 16 21 38 If the house number is one of 10 11 14 16 21 38, then he'll know the ages when he looks at the house number ..... but he doesn't Therefore the house number must be 13, and the ages are either 1 6 6 or 2 2 9 The youngest has red hair, and therefore there is a youngest, and therefore the ages are 1 6 6 A few people won't like the solution to this puzzle. They'll argue that two 2-year-olds can have different ages. If they're twins, nevertheless one is born first. And they might not be twins - one could be barely 2 years old while the other could be only days short of his 3rd birthday. Well, all I can say is this. The house number has to be one of the numbers listed above. And if it isn't 13, then the guy'll know their ages from the house number. He doesn't, and the house number is perforce 13. She tells him that the youngest has red hair. You may not agree that that eliminates the 2-2-9 case and makes the 1-6-6 case the only possible solution. But she obviously thinks so, and he obviously thinks so. Strangely, nobody has ever suggested that this could be a non-Diophantine puzzle (which is a flashy mathematician’s term that means that it doesn't require whole numbers). The ages of little kids are often expressed as “2½” (say), and the values 1½-1½-16 or ½-4½-16 also multiply to 36. Furthermore, 1-2-18 and ½-4½-16 both sum to 21. But I think that we should argue that since she obviously thinks that the existence of a youngest child provides the answer, then 13 must be the house number. Dave
The Ozzy Osbourne of the 34x27
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magicgeorge Inner circle Belfast 4299 Posts |
I hadn't heard that one before. I like it, nicely solved Tomas.
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