An insurance salesperson walks up to house and knocks on the door. A woman answers, and he asks her how many children she has and how old they are. She says I will give you a hint. If you multiply the 3 children’s ages, you get 36. He says this is not enough information. So she gives a him 2^{nd} hint. If you add up the children’s ages, the sum is the number on the house next door. He goes next door and looks at the house number and says this is still not enough information. So she says she’ll give him one last hint which is that her oldest of the 3 plays piano.

Hint: Why would he need to go back to get the last hint after seeing the number on the house next door? Because the sum of their ages ( the number on the house) is ambiguous and could refer to more than 1 trio of factors.

What are the ages of the children?

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Tristan, you are today’s winner!

2, 2, 9If you list out the trio of factors that multiply to 36 and their sums, you get : 1 1 36 = 38. 1 2 18 = 21. 1 3 12 = 16. 1 4 9 = 14. 6 6 1 = 13. 2 2 9 = 13. 2 3 6 = 11. 3 3 4 = 10. Since the number on the house next door is not enough information there must be more than 1 factor trio that sums up to it, leaving two possibilities: { 6, 6, 1} , {2, 2, 9} . When she says her ‘oldest’ you know it can not be {6,6,1} since she would have two ‘older’ sons not an ‘oldest’.

ages 1, 4, 9. The oldest has to be old enough to reach keys & pedal.