Two old friends, Jack and Jill, meet after a long time. here’s the conversation they had:

**Jack:**Hey, how are you man?

**Jill:**Not bad, got married and I have three kids now.

**Jack:**That’s awesome. How old are they?

**Jill:**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.

**Jill:**My eldest kid just started taking piano lessons.

**Jack:**Oh now I get it.

How old are Jill’s kids?

**Possible Solution:**

**Since the product of their ages are 72, let us find the 3 factors of 72 and their sum:**

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

Now since the sum of their ages is Jack’ birthday which can be anything between 1 to 31, so any of the above combination. But since there is ambiguity or since Jack is not able to find the answer, it means it can be obly those combinations whose sum occur more than once in the above factors: 14

That means the answer can be (2,6,6) or (3,3,8)

Now since Jill mentions the eldest, this implies only one is eldest so (2,6,6) combination is ruled out and the right ages are: (3,3,8)

## 0 comments:

## Post a Comment