A census taker interviews a woman in a house. \"Who lives here?\" heasks. \"My h

Question

A census taker interviews a woman in a house. "Who lives here?" heasks. "My husband and I and my three daughters," she replies. "Whatare the ages of your daughters?" "The product of their ages is 36and the sum of their ages is the house number." The census takerlooks at the house number, thinks, and says, "You haven't given meenough information to determine the ages." "Oh, you're right," shereplies, "Let me also say that my eldest daughter is asleepupstairs." "Ah! Thank you very much!" What are the ages of thedaughters? (The problem requires "reasonable" mathematicalinterpretations of its words.)

Explanation / Answer

We want to find the ages of them.
The product of their ages is 36: List all possiblemultiples of 36 using 3 numbers
1 × 1 × 36 = 36
1 × 2 × 18 = 36
1 × 3 × 12 = 36
1 × 4 × 9 = 36
1 × 6 × 6 = 36
2 × 2 × 9 = 36
2 × 3 × 6 = 36
3 × 3 × 4 = 36
She also says the sum of their ages is the sum of the housenumber, but the census taker looks at the house number, thinks, andsays, "You haven't given me enough information to determine theages" When you look at the sums you get the following:
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
This means that he can not figure it out because two of thechoices have the same sum (1, 6, 6) and (2,2,9) which both equal13.
We know that it has to be either one of those choices somoving on to the next hint we have. She tells him that heroldest daughter sleeps upstairs. Since in the case that it is(1, 6, 6) there would be two oldest daughters, and she only refersto one which implies that the ages of her daughters are the otherchoice which is (2,2,9)
Hope this helps. This means that he can not figure it out because two of thechoices have the same sum (1, 6, 6) and (2,2,9) which both equal13.
We know that it has to be either one of those choices somoving on to the next hint we have. She tells him that heroldest daughter sleeps upstairs. Since in the case that it is(1, 6, 6) there would be two oldest daughters, and she only refersto one which implies that the ages of her daughters are the otherchoice which is (2,2,9)
Hope this helps.

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