Blog Post #109: Happy Birthday Magic Maths for Hagit and Leonid!!

Dear Readers,

This article is to wish very happy birthdays to Hagit and Leonid Kerbel, the lovely couple who (several years ago) founded Musica Mundi School, where I have the pleasure of working as the Mathematics Teacher. It’s Leonid’s birthday tomorrow, just one week after Hagit’s birthday.

For Hagit and Leonid
Hagit and Leonid Kerbel, co-founders of Musica Mundi School
Beautiful Musica Mundi School

Leonid and Hagit are not the same age in years; they actually have a uniquely special age difference. Let’s say that they have an age difference of n years, and you can consider n to be a non-zero whole number.

Why is their n uniquely special!? That’s because, in any year (*from when Leonid was just a few years old, and onwards from then), if we multiply Hagit’s age on her birthday in any year by Leonid’s age on his birthday in that same year* and then add on the magical mystery number n, the result will always be a square number.

Hagit and Leonid’s special age difference n is the only non-zero whole number in the Universe for which this beautiful property always holds true.

I like the fact that n matches the number of letters in LOVE: n=4.

Keen Maths enthusiasts can enjoying proving, quite easily, that the product of Hagit’s and Leonid’s ages (on Leonid’s birthdays*) + 4 will always produce a square number.

Here in this article, we’ll just give three examples to illustrate the result:-

(1 x 5) + 4 = 9 = 3 squared

(19 x 23) + 4 = 441 = 21 squared

(43 x 47) + 4 = 2025 = 45 squared.

It’s time for a quick joke…!

Why did the student eat his Music homework!?

It’s because Leonid told him it was a piece of cake!

Leonid, did you laugh a little bit there!?

Assuming that you don’t have to go to hospital after that one (!!), I’d like to finish by wishing you all a very happy weekend now.

With kindest wishes as always,

Paul Motwani xxx

P.S. In a recent photo taken by my wife, everyone has just eaten some delicious cake and is feeling pretty good!

The cake disappeared quickly!

Author: Paul A. Motwani

My name is Paul Motwani, but my colleagues, my students and their parents mostly call me "Mr. Mo"! My middle initial, A, stands for Anthony, because I was born on the official feast day of St. Anthony of Padua, the patron saint of miracles and of lost souls. I love teaching Mathematics and Chess, and giving fun-packed talks and shows in schools and clubs. The popular ingredients of Math, Chess, Mystery and Magic are my "Fantastic Four", and I give prizes too! I am an International Chess Grandmaster, and (loooooong ago!) I was the World Under-17 Champion. I am the author of five published chess books and hundreds of newspaper articles. I live with my wonderful wife and son in Belgium. I also love music, movies and puzzles. I blog at My e-mail address is You can find me on Facebook, too.

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