Because the census collector had to ask another question. If the house number had been 23, there could only be one answer, so he wouldn't need to ask the question. He would have known automatically that it was 3,5,15. Same for 1,5,45. That means that it had to be a house number with more than one possible answer. 21 is the only option.

>But why can't it be 3, 5, 15 and the house number is 23, or 1, 5, 45 - Hse # = 51?
>
>>A 1 year old would be unlikely to answer the door, and assuming the common concept that 15 and 15 are the same age, the answer can only be 3,3,25. I agree that one 15 year old might say "I'm the eldest" but on the assumption that there actually is a correct answer to the puzzle, it has to be 3,3,25.
>>
>>>>>Evan,
>>>>>
>>>>>>Here's a fun one. http://www.boingboing.net/2005/08/24/puzzle_of_the_month_.html
>>>>>
>>>>>This is the entire universe of possibilities (assuming integer ages)
>>>>>
>>>>>

>>>>>a      1       1     225
>>>>>b      1       3      75
>>>>>c      1       5      45
>>>>>d      1       9      25
>>>>>e      1      15      15
>>>>>f      3       3      25
>>>>>g      3       5      15
>>>>>h      5       5       9
>>>>>

>>>>>
>>>>>a can be eliminated because 225 is an impossible age to attain. e g and h can be eliminated because the oldest person is not of legal age to own a home. f could be eliminated because it sums to the same value as e. But I don't see any way to eliminate down to only one of the remaining b, c and d candidate solutions.
>>>>
>>>>They key to moving further ahead is that the cenus taker must ask another question to determine the ages. He already knows the house number (the sum), so he should be able to get the ages, but he can't.
>>>
>>>I don't see it. If the house number is 31 and he's trying to decide between the two that add to 31 the answer to the oldest person question is irrelevant, any one of the three people can have answered the door.