How Old Are My Children?

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.

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22 Responses

  1. gurubai says:

    hii!!!!!!!!!i agree wit 2,6,6 nd 3,3,8.but at d same tym question s not clear many possibilities r der they can b of any ages nd if d birth date s given question would have been more easier lol……!

  2. RJ says:

    Kevin and Mark…

    You’re missing the point of the question. When Bill tells Jack that the product of his kids’ age is 72 and that their ages add up to his birthdate, this info is not enough for Jack to figure out the ages. If Jack’s birthday was on the 15th or the 17th, Jack would know the ages of the kids immediately because there is only one set of ages that fit that particular birthdate.

    if Jack was born on the 15th, then Bill’s kids MUST be 2, 4, and 9.
    if Jack was born on the 17th, then Bill’s kids MUST be 2, 3 and 12

    The fact that Jack was unsure of the ages after Bill gave him the clues, means Jack’s birthdate must be on a date that has more than one possible solution. i.e the 14th. So all the other possible answers do not apply because they all have just one solution for each date.

  3. laxatives says:

    Kevin: The reason you know it must sum to 14 is beacuse jack knows his own birthdate and still doesn’t have enough information to know the kids ages. That means there must be a duplicate combination

  4. BabulBeastly says:

    Nice Logic…….. I like it 🙂

  5. Heh, forget about the probability here. What about adopted kids and twins and (etc)? What if?

  6. Nick says:

    “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.”

    How is this true? Someone clarify this for me.

  7. This is a really cool problem!

  8. Michael says:

    You can’t have 1 ,2 ,36 because the sum of the numbers is 39. There is no birth date that is on the 39th. Therefore, that answer is eliminated.

  9. Aditya says:

    logical reasoning+mathematical puzzle+brain twister+brain tester+brain teasor+quant reasoning+verbal reasoning+hmmmmm….mixture of all in one ques…

  10. Gil Fuchs says:

    there is a missing factoring in the list of possiblities, (1,1,72) with sum 74. although
    this is quite unlikely a spread of ages, mathematically it is still an entry. but it doesn’t really matter, since there isn’t another factoring with the same sum (almost tautologically).

  11. kevin says:

    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…..

  12. kevin says:

    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.

  13. psychoMantis says:

    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????

  14. Jordi says:

    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.

  15. Mike says:

    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 🙂

  16. Rosario says:

    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

  17. rak says:

    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

  18. JP says:

    I agree with Mark. 2, 6, 6 is still also a valid answer and cannot be eliminated “since there are two eldest ones.”

  19. Mark says:

    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.

  20. Aswin says:

    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.

  21. Robin says:

    Couldn’t you have 1, 8 and 9?

  22. The information presented is top notch. I’ve been doing some research on the topic and this post answered several questions.

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