Blog Post #102: Happy Birthday Wishes Amplified for Romy H., with thanks also to Tessa VG.

Dear Readers,

I am very grateful for still being able to hear pretty well, thanks to having wonderful hearing aids from Amplifon.

Grateful for Hearing

Living in Belgium, I have already received lots of excellent, expert care from former/current Amplifon employees including Anais, Elena L., Romy H. and Tessa VG.

Amplifon experts Romy H. & Tessa VG.

Let’s wish Romy a super happy birthday today,

Scrumptious level Amplified!

and we can all enjoy an original puzzle involving Romy’s favourite one-digit number together with Tessa VG’s different favourite single-digit number. Let’s denote the favourite numbers by R and T respectively.

In the spirit of good fun, the ladies have allowed me to tell you a bit more…! The two-digit number RT (meaning not R x T, but rather the two-digit number with digits R and T in normal base ten) is equivalent to 111 in base T.

One possibility might have been 13 (in normal base ten) equals 111 in base 3, because 1113=1+3+32=13ten. However, the true solution for the ladies’ RT is not 13, but something else…

Your fun challenge is to now figure out the precise values of R and T. Then calculate R2 to discover Romy’s new age today!

The puzzle answers will be given in just a few M😊ments…

First, something I left until right here, here are a couple of classic ear jokes to hear!!

What three ears did Captain Kirk have?

His left ear, his right ear, and the final frontier!

How much does it cost a pirate to pierce his ears? – A buccaneer!!

Oh, wait…Captain Kirk just told me a third one…!

What did the left ear say to the right ear…?

Between us, something smells…

…goodness knows, goodness nose what!

How tricky is it to eat chocolate gateaux?!…

…It’s ‘a piece of cake’!

Here’s wishing Romy 100% joy. She’s turning 100 today…but only in number base R !! 😊😊

Romy’s Birthday Brainteaser Solution

Given earlier that 13 is NOT the correct value of RT, the only remaining possibility that will actually work is RT=57. (Full mathematical details about the ladies’ favourite numbers are given below, near the end of this post**.)


T=7 & R=5.

Romy’s new age today is R2=52=25.

To almost round off this 100% good fun, happy birthday blog post, 100five=0+0+52=25ten.

Happy birthday, R😊my=25 today!

Wishing everyone a super Sunday now, with your happiness well Amplified!

Paul M😊twani.

P.S. **Here come the full mathematical details explaining why RT=57

The Fascinating World of Mathematics

We were given earlier that the two-digit number RT (meaning not R x T, but rather the two-digit number with digits R and T in normal base ten) is equivalent to 111 in base T.

R is the tens digit, and T is the units (or ones) digit. So in fact, the base ten value of RT is really 10R+T.

The total base ten value of 111 in base T, or of 111T, is 1+T+T2.

Therefore, 10R+T = 1+T+T2 .

That simplifies slightly to give 10R = 1+T2 .

In words, that’s telling us that some multiple of ten is one more than some square number.

By considering 10, 20, 30, 40, 50, 60, 70, 80 and 90, in which 10=1+9=1+32

and 50=1+49=1+72, we can deduce that RT=13 or 57.

However, since we were told earlier on that RT does not equal 13, the only correct solution remaining now is RT=57.

B😊nus: Romy’s birthday is of course day number sixteen, today, of calendar month #5. In just another 7 months + (7+7-5) days from now…I look forward to saying “Merry Christmas” on 25 December!

In the meantime, for a bonus word puzzle now, and to conclude in a very merry way for Romy, can you read my mind and see which two words (with 3 letters followed by 6 letters) I’m thinking of by rearranging the letters of MERYTESSA !? 😊😊

There are surely numerous possibilities, but my fun personal ones are:




Listen well, and many things will become clearer

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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