Blog Post #83: Magical Duets!

Dear Readers,

My house number, 11, is a palindrome; so is 101 or 11 x 11 =121, but what about 11 x 101 x 11? The result 12221 is clearly palindromic, and it’s intended to let you know a very nice date for your diary: exactly three weeks from today, on 12.2.21, you’ll be able to enjoy on YouTube (at 19:30 Central European Time via and clicking on the banner there) a feast of fabulous, musical solo performances featuring many young talents of Musica Mundi School.

I have the pleasure of getting to teach Mathematics to every student who studies the subject at the school, and right now I have some delightful surprises starring Julija and Hoi Yuet.

We’ll start by listing all the letters from H to O in the English alphabet:

H  I  J  K  L  M  N  O

Now, take out from there the letters which occur in JULIJA or HOI YUET.

So, we take out H, I, J, L & O, and that leaves us with:

K  M  N

The next step is to note the numerical values of each letter according to their positions within the alphabet…

11  13  14

…and now we’ll multiply those numbers together and then add 5 because we took out 5 letters (H, I, J, L & O):

11 x 13 x 14 + 5=2007, the year when Julija was born!

I WAS BORN = RAINBOWS is one of my favourite anagram ‘word equations’!

The students like number tricks such as how to mentally calculate 45 squared in about one second! To calculate 45 x 45, think: “Digit 4 at the start x the next whole number, 5, makes 20; also 5 x 5 = 25; the final result is 2025.” That’s very handy for super-speedy squaring of whole numbers ending in 5.

What about now calculating 41 x 49 really quickly!?

I like various possibilities, including this one:

41 x 49=(45-4) x (45+4)=45 squared – 4 squared=2025-16=2009, the year when Hoi Yuet was born!


That funny, second anagram ‘word equation’ was inspired by the fact that one of the libraries within Musica Mundi School is named after George Sand, the pen name of the famous French novelist and journalist Amantine Lucile Aurore Dupin (1804-1876).

Some quotes that I love about books include the following:

“I kept always two books in my pocket, one to read, one to write in.”-Robert Louis Stevenson

“There is more treasure in books than in all the pirates’ loot on Treasure Island.”-Walt Disney

“You know you’ve read a good book when you turn the last page and feel a little as if you have lost a friend.”-Paul Sweeney

Over the last few days, Julija has been telling me about a beautiful book that she is reading in Slovenian. For me, she translated the title to ‘The Quiet Land’. One of the main characters is a teenaged girl named Eliana, who has a younger brother named Joseph.

Having also been told Eliana’s and Joseph’s exact whole number ages by Julija, I can now give you this lovely brainteaser:

If we multiply Eliana’s age by Joseph’s age, the product result is actually a square number and also a cube number. How old is Eliana, and how old is Joseph?

Given that Eliana is a teenager and Joseph is younger, the solution is a unique one, and is given down below, at the end of this article.

However, what other possibilities could there have been if I had said that the product of Eliana’s age and Joseph’s age is a square number but not a cube number?

Furthermore, what other possibility could there have been if I had said that the product of Eliana’s age and Joseph’s age is a cube number but not a square number?

At least one of the school’s cats seems to have a liking for Maths!

Fun brainteasers starring students and the cats could be coming soon…!

In the meantime, I wish everyone a wonderful weekend now.

With very best wishes as always,

Paul Motwani xxx

P.S.=Puzzle Solutions!

Eliana is 16 and Joseph is 4;

16 x 4 = 64 = 8 squared or 4 cubed.

(Other possibilities would be 18 x 2 = 36 = 6 squared or 16 x 1 = 16 = 4 squared if we just needed a square number result; or 18 x 12 = 216 = 6 cubed if we just needed a cube number result.)



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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