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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The information presented is top notch. I’ve been doing some research on the topic and this post answered several questions.
Couldn’t you have 1, 8 and 9?
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.
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.
I agree with Mark. 2, 6, 6 is still also a valid answer and cannot be eliminated “since there are two eldest ones.”
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