I came up with this idea/sequence/problem while having my hair cut the other day (don’t ask me why), and haven’t been able to explain the math behind it ever since. Here’s how it goes:

If one of your parents’ (let’s take your father as an example) age was a multiple of 9 when you were born, then your ages follow an interesting sequence. Let’s say I was born when my dad was 27.

Then, when my dad is 30, I am 03.

When my dad is 41, I am 14.

When my dad is 52, I am 25.

When my dad is 63, I am 36.

And so on.

It turns out that, for the case in which your parent’s age was a multiple of 9 when you were born, your ages are flipped numbers (25 <–> 52) every 11 years. Additionally, the sequence first starts when your age equals your parent’s age at the time when you were born, divided by 9. In the example above, the sequence starts when I am 27/9 = 3 years old.

Is it possible to derive the logic of this sequence analytically? Since there’s no simple math operator that flips numbers around (i.e. 36 <–> 63), it made me intrigued as to why/how this sequence is possible in the first place.

Let me know what your thoughts are!