I had to help a high school kid solve this problem yesterday. It’s pretty interesting I think.

I sent it around the team and people seemed to enjoy it so here you go. (In the old days, I would have saved this puzzle for an interview question, but pure puzzle questions are discouraged now.)

A census taker knocks on Mary’s door.

Census Taker: I need to know the age of your three children

Mary: The product of their ages is 36.

Census Taker: hrmmm

Mary: The sum of their ages is the same as my house number.

Census Taker: I still don’t have enough information.

Mary: The younger two are twins

Census Taker: Ok, I’ve got it now.

What are the ages of Mary’s children?

ANSWER IS NOW IN THE COMMENTS (along with a afterschool special style wrapup of what we've learned).

what is the answer?

twins:3,3

other: 4

3*3 = 9

9 * 4 = 36

Since we don’t know the home’s address, there is not enough information to solve. Possible answers are:

1, 1, 36 (unlikely, but with modern science…)

2, 2, 9

3, 3, 4

6, 6, 1

At the risk of being pedantic, technically a product is the result of only two numbers multiplied together.

Can be either 2,2,9 or 6,6,1.

From the first hint, you now that the possible combinations of ages are:

1,1,36 (sum=38)

1,2,18 (sum=21)

1,3,12 (sum=16)

1,4,9 (sum=14)

2,2,9 (sum=13)

2,3,6 (sum=11)

3,3,4 (sum=10)

6,6,1 (sum=13)

From the second hint, you know that the sum of the ages is NOT unique, otherwise the census taker would have known the correct answer at this point. This leaves you with:

2,2,9 (sum=13)

6,6,1 (sum=13)

The hint about being twins doesn’t help much, since both these combinations involve twins. If the hint stated that "the younger two are twins" or "the older two are twins", then you would be able to narrow it down to one answer. As it is, I’m stuck 🙂

Still not enough info.

Q1: Product = 36

A: 8 combinations of ages that work:

36, 1, 1

18, 2, 1

12, 3, 1

9, 4, 1

9, 2, 2

6, 6, 1

6, 3, 2

4, 3, 3

Q2: Sum = my house number

A: The salesperson knows the house number so this would normally be enough to get the answer, but two combinations have the same sum (13):

9, 2, 2

6, 6, 1

so it must be one of these two, and the house number must be 13

Q3: Two of them are twins

Unfortunately, both 9,2,2 and 6,6,1 would satisfy this condition.

Are you sure it wasn’t "the older ones are twins" ?

Doh! Beat me by *that* much….

Was the post edited??? Now it says the "younger two are twins". Finishing off my earlier comment, that leaves you with 2, 2, and 9 as the ages of Mary’s children.

I have to fess-up though, I actually WAS asked a very similar question when I interviewed with MS, but got it wrong at the time. Maybe that’s why the didn’t hire me 🙂

Nice work folks. I editted the problem description to be "the younger two are twins" which was my screw up. The mistake most people (such as myself) is to ignore the sequence of information. We engineering types tend to extract out the facts from the statements and accidentally lose what might be important information because the mental model we build the first time is the wrong model.

When I solved it, I immediately wrote:

A*B*C=36

A+B+C=X

B=C

substituted and got stuck. Ironically, I then thought… well, heck, public school teachers must have gotten this from somewhere so I searched for it on the internet. The answer I found was… COMPLETELY WRONG. But it did make me think about the problem again.

And now you know, and knowing is half the battle. Go JOE! (interestingly enough, the other half of the battle is gouging)

answer is 9,2,2 as 6,6,1 does not correspond to the fact that the twins are youner….

riddled, that’s ironic. I went to interview training recently and these sorts of "Ah HA!" questions are discouraged now. People (rightfully in my opinion) complained that whether they can solve one frustrating puzzle on one particular day is potentially really insulting and left a bad taste in people’s mouths about the company. If it makes you feel any better, I know a lot of people much smarter than myself who can’t solve it.

There is NO NEED to add "younger" to the puzzle. If you take the fact that twins means same age, there are 3 possibliites:

3,3,4

2,2,9

6,6,1

The next hint is that the sum of ages is Mary’s house number. Why would the puzzle even mention it? I think the reason is to indicate that the sum of ages has to be UNIQUE. Since 6,6,1 and 2,2,9 both add up to 13, the only logical conlusion is that the age of the kids is 3,3 and 4.

Steve,

If the answer were 3,3 and 4. The census taker could have gotten the answer after the second fact because *he* knew the house number and there is only one combination of factors of 36 that equals 10.

"(In the old days, I would have saved this puzzle for an interview question, but pure puzzle questions are discouraged now.)"

That’s ironic, ’cause I once got that question in a Microsoft interview. 🙂

Wow. Now I see how it destroys MSFT productivity, LOL!

haha. Yeah, the profiler team productivity cost of this exercise is at least half a man-day already. I never did see the kid’s assignment sheet. This problem could have been a Linux or Apple plant to destroy us from within.

I think the answer can change if you permit fractional ages (i.e. "The twins are each two and a half years old").