Old friends and children – a matter of memories and maths

26 Sep 2016

“Why are maths books always unhappy?” “Why?” “Because they have lots of problems.” ”Hahaha! Amazing...” Image: maradon 333/Shutterstock

If you ran into an old friend, would you tell them your big news via maths puzzles? No? You’re clearly not Alice or Bob.

Alice and Bob were very good childhood friends. One day, having not seen each other for years, they run into each other in the city.

Reminiscing about the good old days, the pair remember (among other things) the fun they used to have in maths class at school.

Future Human

When Alice asks Bob about his family, Bob tells her that, for old times’ sake, he’ll answer in the form of a maths puzzle.

“If you add up the ages of my three children, you’ll get today’s date, not including month or year. The product of their three ages is 36,” says Bob.

“Hmm,” says Alice. “Not sure that’s enough information for me to figure out their ages.”

“Would it help if I told you that the youngest is with Grandma right now?” asks Bob.

“Yeah, it does. I know their ages now.”

“Prove it,” says Bob.

How does Alice prove it? And how old are Bob’s kids?

Scroll down for the solution to this week’s puzzle.

Maths: young maths whizz

One of Bob’s kids, probably. Image: Evgeny Atamanenko/Shutterstock.com


The youngest child is one year old and the older two are six-year-old twins.

Alice knew that there are several ways in which to write 36 as a product of three numbers:

1 x 2 x 18
1 x 3 x 12
1 x 4 x 9
1 x 6 x 6
2 x 2 x 9
2 x 3 x 6
3 x 3 x 4

When we add up the three factors in each of these products, we get the values 21, 16, 14, 13, 13, 11, 10.

Assuming that the maths excitement hadn’t gone to Alice’s head and she knew what day of the month it was, there was no logical reason for the information given by Bob to not be enough to figure out the children’s ages.

The only way there could have been confusion is if Alice and Bob had bumped into each other on the 13th of the month. In this case, there would be two possible sets of ages for the children: 1, 6 and 6, or 2, 2 and 9.

Knowing that Bob had a “youngest” – rather than ‘the two youngest’ – Alice is able to deduce that Bob’s kids are 1, 6 and 6.


Updated, 4.35pm, 30 September 2016We originally left out a crucial part of this week’s puzzle: half of the question. We apologise to absolutely everyone. But look on the bright side – at least now you get to solve it twice!

Kirsty Tobin was careers editor at Silicon Republic