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A man taking the census walks up to the apartment of a mathematician and asks him if he has any children and how old they are.

  1. The mathematician says: "${\it\mbox{I have three daughters and the product of their ages is 72}}$".
  2. The man tells the mathematician that he needs more information, so the mathematician tells him ${\it\mbox{"The sum of their ages is equal to our apartment number"}}$.
  3. The man still needs more information so the mathematician tells him ${\it\mbox{"My oldest daughter has her own bed and the other two share bunk beds"}}$.
Felix Marin
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Shaina
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    What's the apartment number? – muffle Nov 25 '13 at 23:29
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    Are we supposed to assume that the census-taker has enough information after the mathematician's last answer? Also, you should put the question in the question body, even though it is already in the title. – Trevor Wilson Nov 25 '13 at 23:29
  • Is the fact that they two youngest daughters share a bunk bed supposed to imply that they are twins? – Git Gud Nov 25 '13 at 23:31
  • Yes, I'm pretty sure that implies they are twins. – muffle Nov 25 '13 at 23:31
  • I vote $3,4,6$ with apartment number $13$... – abiessu Nov 25 '13 at 23:34
  • Is the census-taker a 'perfect-logical' being in the sense that he can always deduce everything that there is to be infered and is he incable of lying? For instance, when he says he doesn't have enough information, is that necessarily true? – Git Gud Nov 25 '13 at 23:35
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    I don't think the mathematician's last statement is supposed to imply that the youngest two daughters are the same age, only that there is a unique oldest daughter. – Trevor Wilson Nov 25 '13 at 23:49
  • @muffle got the right idea. – Felix Marin Nov 26 '13 at 02:11

2 Answers2

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By examination, there are $12$ integer triplets that multiply to $72$.

Ten of them have unique sums, so if any of these were the solution, the census taker would not be in ignorance of the triplet, once he knew the sum

Two triplets, $(2,6,6)$ and $(3,3,8)$ both add to $14$. Once the professor implies that he has an oldest daughter, the choice is uniquely defined...

Edited to correct inability to count rows in a spreadsheet....

DJohnM
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I cannot think of anything really elegant. Just write down all possible ways of writing 72 as a product of three numbers. Then write the sum of each triplet. The correct answer would be that triplet in which the smallest number occurs exactly twice and no other triplet with this property exists whose sum is same as the sum of elements in this triplet.

Priyatham
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