## Mirror ages brainteaser

By David Shaw, 3 March 2021

Misrak was looking at the birthdays in her family. After a bit of maths, she realised that her father’s age and her grandfather’s age had the same digits, but swapped.

When she added their ages together, she got 121. Her grandfather was aged between 20 and 40 when her father was born.

Can you work out how old her father and grandfather are?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

• Half of 121 is 60.5, so Misrak’s grandfather is older than 60 and her father is younger than 61.

• To start off, you could try to get the ones digit to work and move on from there.

** **

## Brainteaser answer

Let’s start by looking at the ones digit of the ages. We know that the sum of the ages has a ones digit of 1. The ages can’t end with 1 and 0, because swapping digits won’t work. That means the ones digits must add to 11.

We can list all the possible pairs of last digits that add to 11: 5 and 6, 4 and 7, 3 and 8, 2 and 9.

If we know the last digits of both ages, we can work out what the ages are. For example, if the last digits are 5 and 6, the ages are 56 and 65. These add to 121, but this isn’t a good solution because Misrak’s grandfather would only be 9 when her father was born.

If the last digits are 4 and 7, we get 47 and 74 as ages. That adds to 121, indicating Misrak’s grandfather was 28 when her dad was born, so this is a solution that works.

For the remaining pairs, the age gap between father and grandfather more than 40 years: 83 – 38 = 45, and 92 – 29 = 63. We know that’s not the answer because Misrak’s grandfather was aged between 20 and 40 when her father was born.

So Misrak’s father is 47 and her grandfather is 74.

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5 March, 2021 at 12:36 pm

I love CSIRO educational stuff, I really do. I’ve given subscriptions to nieces & nephews, and then to my own two sons. They’ve both outgrown the magazines, but I still love receiving the emails and often challenge myself with the brain teasers for fun. But I really take exception to the incredibly ageist tone in the answer to this week’s brain teaser. It’s offensive. To me, to my sister, to other immediate and extended family members, and to many friends whose fathers were older than 28 years when they fathered children. This loads of bollocks serves only to feed ridiculous notions and shame those children whose parents decided to procreate in their 30’s, 40’s, 50’s, and beyond.

In fact, the ABS states that “Between 1990 and 2010, the median age of fathers of nuptial births increased by almost three years, from 31.4 to 34 years…”

Shame on you and your outdated views, CSIRO. Please do better next time.

“…Misrak’s grandfather was 28 when her dad was born, so this is a good solution {EXCUSE ME??}.

For the remaining pairs, the age gap between father and grandfather is too big {HOW VERY JUDGEMENTAL OF YOU ?}. 83 – 38 = 45, and 92 – 29 = 63.”

5 March, 2021 at 12:42 pm

Hi Margie,

Sorry for any offense we caused! The intended value judgement was merely that the solution work with the age restriction in the question:

Her grandfather was aged between 20 and 40 when her father was born.

I’ll adjust the words slightly to make it a bit clearer.

7 March, 2021 at 7:03 am

Appreciated, thank you ??