# Find the age

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John has three sons and his friend Jacob wants to know their ages. John gives him three hints as Jacob could not answer till the third hint :–

1. The product of their ages is 72
2. The sum of their ages is the same as my house number
3. The oldest of sons love chocolate ice cream

SherlockHolmes Expert Asked on 8th November 2019 in

Ages 6, 6, and 2

Seeker008 Expert Answered on 10th November 2019.

72 has the following factors 2*2*2*3*3

With these factors the following age combinations can be made:
1+1+72 = 74
1+2+36 = 39
1+3+24 = 28
1+4+18 = 23
1+6+12 = 19
1+8+9 = 18
2+2+18 = 22
2+3+12 = 17
2+4+9 = 15
2+6+6 = 14
3+3+8 = 14
3+4+6 = 13

Only two of them have the same sum: 2,6,6 and 3,3,8
With all the other combinations Jason would have known the answer with only the first two hints.
The last hint says that John has an oldest son.
With the ages 2, 6 and 6 John would have two “oldest sons”

So the correct answer is 3, 3, and 8.

CugelTheWise Expert Answered on 11th November 2019.

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