# Answer to PopSci 1960 puzzle

Well over 600 people submitted answers to the puzzle I posted yesterday. Most of the answers (90% or so) were incorrect. Andy Wood was the first to give the correct answer along with the correct reasoning:

Here are all the possible ways of factoring 225 into three integers:

9 + 5 + 5 = 19

15 + 15 + 1 = 31

15 + 5 + 3 = 23

25 + 9 + 1 = 35

25 + 3 + 3 = 31

45 + 5 + 1 = 51

75 + 3 + 1 = 79

225 + 1 + 1 = 227

Only two of those sums are the same, so the address of the house must
be 31, as it would be the only scenario in which the census taker
would need any additional information.  Presumably the implication is
that if the solution had been 15, 15 and 1, the person answering the
door would have said that there was another person his age, not that
he was the eldest, so the answer is 25, 3 and 3.

Reader comment: Marc Kelsey says: "Here's why I think the answer to the 1960's puzzle is bullshit:

"If the census taker had to ask the person at the door if they were the
oldest, it must have been because he couldn't tell whether the person at
the door was the oldest or not. If he had been talking to a 25 years
old, and the others in the house were presumably 3 and 3, he would not
have had to ask. Therefore, he was talking to a 15 year old, and wanted
to know whether they were the oldest 15 year old (by a month, say), or
the youngest 15 year old.

"In other words, the question is wrong, not the answers."

Reader comment: Mark Jaquith says: "Regarding Marc Kelsey's response.

"The census taker asked because he didn't know whether the person he was talking to was 25 or 15. That may be a wide swath of years, but what if someone looks about 20, and must be either 15 or 25? Also, if the census taker believes the person at the door to be 15, why not the 15 year old from the 15 + 5 + 3 set? Because the census taker says that he needs more information, it must be because he is undecided between two sets that add up to the same house number.

"Rather, the strongest objection relates to the definition of "eldest." If there are two 15 year olds in the house, one of them MUST be older, even though their integer ages are the same. But, if the person at the door is the older of the 15 year olds, and he answers "yes" (that he is the oldest), the riddle is unsolvable, as both the older of the two hypothetical 15 year olds and the 25 year olds are the oldest of their respective sets. You must consider that the person proposing the riddle (the person at the door) knows this, and would not give an answer that would leave the riddle unsolvable, and would answer by saying that there is another person of their age in the house, or simply answering "no" (because they are the same integer age). If the person at the door says they are the oldest, it must mean they are 25, because that answer would leave the riddle unsolvable if they were 15.

"Admittedly, it would be better if the riddle had the person at the door had say "no," because then there is no doubt at all that the person is 15. Of course, then you have to consider the oddity of two 15 year olds owning a house and raising an infant."