Question: Two old friends, Jack and Bill, meet after a long time.
Three kids
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That’s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool… But I still don’t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.
How old are Bill’s kids?
Answer: Let’s break it down. The product of their ages is 72. So what are the possible choices?
2, 2, 18 – sum(2, 2, 18) = 22
2, 4, 9 – sum(2, 4, 9) = 15
2, 6, 6 – sum(2, 6, 6) = 14
2, 3, 12 – sum(2, 3, 12) = 17
3, 4, 6 – sum(3, 4, 6) = 13
3, 3, 8 – sum(3, 3, 8 ) = 14
1, 8, 9 – sum(1,8,9) = 18
1, 3, 24 – sum(1, 3, 24) = 28
1, 4, 18 – sum(1, 4, 18) = 23
1, 2, 36 – sum(1, 2, 36) = 39
1, 6, 12 – sum(1, 6, 12) = 19
The sum of their ages is the same as your birth date. That could be anything from 1 to 31 but the fact that Jack was unable to find out the ages, it means there are two or more combinations with the same sum. From the choices above, only two of them are possible now.
2, 6, 6 – sum(2, 6, 6) = 14
3, 3, 8 – sum(3, 3, 8 ) = 14
Since the eldest kid is taking piano lessons, we can eliminate combination 1 since there are two eldest ones. The answer is 3, 3 and 8.
Related posts:
we cannot say that a person starts learning piano lessons only at the age of 8. It might also be 7 or 10 or even 12.
Are we supposed to read the mind of Bill…?? LOL…..
This is really a stupid question! Any one combination of the following is possible…
2, 4, 9 – sum(2, 4, 9) = 15
2, 3, 12 – sum(2, 3, 12) = 17
3, 4, 6 – sum(3, 4, 6) = 13
3, 3, 8 – sum(3, 3, 8 ) = 14
1, 8, 9 – sum(1,8,9) = 18
1, 6, 12 – sum(1, 6, 12) = 19
OK…we can eliminate this 5th answer since both the elder kids are nearly of the same age…. However, you cannot pick up anything as the correct answer since all of them suit…..
The question must be a wrong one.
This is a stupid question, how am I supposed to know Jack is not a moron and just can’t figure this out instead of the fact that there are two possible solutions that match his birthdate????
to Lacho.
72 decomposed to smallest divisors (prime numbers and 1):
1, 1, 2, 2, 2, 3, 3,
*(since the are 3 kids, 1 can be used 2 times).
And you divide this divisors to 3 sets and use all of them to have product 72 so you get the table.
Anyway I agree with Mark. Just lets say, there is 9/12 probability of 8,3,3 and only 3/12 of 2,6,6 of asking in this partcular date part of year. And even probasbility kids are not older then 12 months is lower. But is same asi for 3,3 in 3,3,8.
I stopped at 2,4,9
Lacho, the kids ages are integers, so find multipliers that equal 72, and work backwards, 8 x 9 = 72, then find multipliers to equal one of those 3,3,8, 1, 8, 9, or 2,4,9 all work. As pointed out in the comments 2,6,6 equals 72, but it’s debatable, you might argue one is older by a few hours
I know this might seem stupid to you guys but i was thrown off with the birth date. my birth date is 5th. so when he says the same as your birth date….??? confused for sure
3 3 8 because 2 2 6 and 3 3 8 gives same sum if it is other than this we wouldnt ask other hint as he knows his birth date
I agree with Mark. 2, 6, 6 is still also a valid answer and cannot be eliminated “since there are two eldest ones.”
I object. A man can have 2 kids that are both 6 years old and still have an oldest. They could be 9-11 months apart but we’d still call them both “6″ for at least part of the year. Therefore the fact that there’s an oldest doesn’t differentiate the 2 remaining options at all. More of a linguistic objection than a logical one, but if you’re going to phrase the question as a conversation you’ve got to play by the rules of the medium.
You are right. We should count 1, 8 and 9. However, it would not have made a difference in the solution.
Thanks for pointing it out. I will correct it.
Couldn’t you have 1, 8 and 9?
The information presented is top notch. I’ve been doing some research on the topic and this post answered several questions.