Here's a quiz you can't Google for...

[Admin]

This one is a graphic and I don't think there's an answer on Google. :P

http://www.ukskeptics.com/graphics/census_puzzle.jpg

So, what are their ages and what is the house number?

[Araneus]

225 has factors 3x3x5x5, which means they could be (5, 5, 9), (3, 3, 25) or (3, 5, 15). The house number would be 19, 31 or 23 respectively, but since it is not given I don't see how it can have a bearing on the answer. Perhaps the fact that he had to ask whether the person was the eldest indicates (5, 5, 9), because in the other cases it would have been obvious, however it seems unlikely that a house could be populated entirely by children, so maybe (3, 3, 25) is the answer.

[median]

This one is a graphic and I don't think there's an answer on Google


Who says? ;D

http://www.boingboing.net/2005/08/25/answer_to_popsci_196.html

[Araneus]

Whoops, didn't consider the non-prime factors. Seems like there is debate over which is the correct answer though, based on differing interpretations of the need for the census-taker's "are you the oldest" question.

[Admin]

I think the title must have been as much a Google challenge as much as a quiz! ;D ;D

Silver star to Araneus for getting straight to the correct method of solving it.

Yes, only a silver star. :P

Isn't it funny how people read more into these questions than there's really there? I mean suggesting the answer is wrong as the man would have been able to guess how old the person was without asking etc. ::)

[Araneus]

Isn't it funny how people read more into these questions than there's really there? I mean suggesting the answer is wrong as the man would have been able to guess how old the person was without asking etc. ::)

I think it's a reasonable point of contention though -- clearly the fact that the census taker asked "Are you the oldest?" is supposed to provide some information which helps in solving the puzzle, and it appears to be ambiguous as to what that information is. If the ages are (25, 3, 3), as the "official" answer seems to be, it is pretty bizarre that he would ask this question, since nobody could mistake a 25-year-old for a 3-year-old.

[Admin]

The point is that they're not real people - it's simply a logical puzzle - yet people will insist on saying the answer is wrong or flawed because "the man" could have guessed the person's age by looking etc.

He couldn't, 'cause he isn't real!! ;D

[Araneus]

Yes, but in this particular case speculation about what "the man" did or did not know is a critical part of the solution. It is still not obvious to me what the purpose of the "Are you the oldest" question was, and which of the two possible outcomes it points to.

[Admin]

Here's my reasoning:

The possible factors of 225 are:

1 x 3 x 75
1 x 5 x 45
1 x 9 x 25
1 x 15 x 15
3 x 3 x 25
3 x 5 x 15
5 x 5 x 9

They are the possible combinations of ages.

Adding them up (to reveal the house number) gives:

1 + 3 + 75 = 79
1 + 5 + 45 = 51
1 + 9 + 25 = 35
1 + 15 + 15 = 31
3 + 3 + 25 = 31
3 + 5 + 15 = 23
5 + 5 + 9 = 19

So, if the house number was 51 then the residents would have to be 1, 5, and 45 as there is no other option.

As the census taker knew the house number but was still unsure of the ages, the house number had to be 31; hence the ambiguity.

He then asked "are you the eldest?" and the reply was yes.

The possibilities for 31 are:

1 + 15 + 15 = 31
3 + 3 + 25 = 31

If there's an eldest, their ages must be 3, 3, and 25.

[Araneus]

If there's an eldest, their ages must be 3, 3, and 25.

See, that's the part I'm not convinced about. Two 15-year-olds are not necessarily twins, so there could still be an older and a younger of the pair. Therefore the "yes" answer could apply in both cases.

[Cuddles]

See, that's the part I'm not convinced about. Two 15-year-olds are not necessarily twins, so there could still be an older and a younger of the pair. Therefore the "yes" answer could apply in both cases.


And even if they are twins, one must be the older twin. I suppose the point is that you have to pick holes in the riddle to be able to question it. Yes, it isn't 100% factually accurate, but as a riddle it should be obvious what it means. It is simply a number puzzle using integer numbers. If you have to argue about human nature and fractions of ages you can be fairly sure you're barking up the wrong tree. The official answer is the obvious one and to get a different answer or to make it unanswerable requires more arguing and should be eliminated by Occam.

[Araneus]

Yes, it isn't 100% factually accurate, but as a riddle it should be obvious what it means.

Well it's certainly not in the least bit obvious to me. Even the "official answer" is based on guesswork:


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,

That's not a valid presumption in my book. Even if his sibling was the same integer age, the question would still have made sense and the boy could have answered it in the same way.

[Cuddles]

Well it's certainly not in the least bit obvious to me. Even the "official answer" is based on guesswork:

It's not guesswork, you just have to understand what the riddle is actually saying :

"Find three integers that have a product of 225 and have a non-unique sum such that the additional information that the greatest one is unique is required for a unique solution."

That is what it actually says. It is a number problem about numbers. To form it into a more obscure riddle with a human perspective the wording is changed, but that is still what it actually means. This is not a question about what the cencus man is thinking or how twins would answer certain questions. It is exclusively about maths. Taken as a maths problem there is a single correct answer. The problems of translating pure maths into the real world and back does not mean any of it is based in guesswork, it simply means you have to understand that that is what you are trying to do when solving this riddle.

[ali_baba]

that seems more appealing but still i think that maths should not be completely isolated with simple logical facts as was the case in this question

to put it simply more information should have been given to ascertain 3,3 and 25 answer

[godgutsguns]

We are losing sight of the chief aim/s of a logic puzzle. Logic puzzles are not just about maths, but language as well. If it were only about maths, it would be formulated numerically.

I agree that a logic puzzle is worthless if it is even slightly able to be seen as double-edged; even so, I believe that this puzzle is a decent one.