Blog Post #11: Good Secrets

Dear Readers,

Would you like to try a fun experiment right now? I’m guessing that you weren’t expecting such an opening line, yet I’m optimistic that you’ll say “Yes”! So, please do read on to discover more…

Step 1: Think of a seven-letter English word that is the correct name for the beautiful cup in the picture.

Step 2: Remove the first two letters from the seven-letter word.

Step 3: I’m hoping that the five letters you’re left with now spell a girl’s name. Which world-famous 19th-century male author might you be reminded of by the girl’s name?

OK, let’s verify whether you know my secret answer!

I’m happily confident that you also thought of CHALICE→ALICE→ALICE IN WONDERLAND by LEWIS CARROLL.

The writer is probably best known by his pen name, though he was actually Charles Lutwidge Dodgson (1832-1898), and he was an Anglican deacon, a keen photographer, and a highly creative mathematician. My personal favourite quote of his is the following: “One of the secrets of life is that all that is really worth the doing is what we do for others”–Lewis Carroll. Here is another of my absolute favourite quotes about secrets. “My secret is simple–I pray”–St. Mother Teresa of Calcutta.


The next surprise on today’s menu is a math trail where we’re going in search of a unique, secret, two-digit whole number…To introduce this part of our adventure, let’s start with my age, 55. Can you figure out exactly what I’ve done in order to generate the sequence 55→25→10→0?

Sincere congratulations if you discovered that I kept multiplying digits together. From 55, I did 5×5 to get 25, and then 2×5 to get 10, and finally 1×0 to end with 0. In our math trail, sequences stop when we get down to a one-digit number (anything from 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9).

The sequence starting with 55 contained a total of four numbers: 55, 25, 10 and 0. Your special, fun challenge is to find which new two-digit number I am now secretly thinking of. I will give you this golden clue: the new sequence will have a total of five numbers, and my secret number is the only two-digit number which can lead to a sequence of five numbers. If you start with any other two-digit number, your sequence will be shorter. So, can you discover my secret sequence? Happy hunting now!



Seeing the title just above might well make chess players think of former World Champion Boris Spassky.

In fact, though, I am now thinking of another very fine gentleman, namely Boris Gelfand, who is of course also a truly world-class grandmaster. The fact that Boris shares a lot of his experiences and chess secrets in his “Positional Decision Making In Chess” and “Dynamic Decision Making In Chess” (published respectively in 2015 and 2016 by Quality Chess UK Ltd.) is surely benefitting thousands of keen players around the world, who are aiming to improve and are perhaps also aspiring to become great champions.

To let you see the book covers here, while at the same time providing you with a couple of puzzle positions that I was recently using myself as training exercises (not actually from inside the books, though), I’ve merged photos as follows.

It is Black to play and win in the first puzzle.

It is White to play and win in the second puzzle.

Chess Thinking & Training


Why are celebrities so cool…?

It’s because they have so many fans!

Yes, fans!

Feeling nice and cool!



Notice that “lucky” 21, for example, can’t possibly be my unique secret two-digit number because it would duplicate the same numbers that would result from its reverse 12, since 2×1=1×2=2 in each case. 21→2 and 12→2, directly finished. That instructive example can help us to realise that, because my secret number is unique–one of a kind–it must be the same number as its reverse. That immediately and dramatically cuts down the list of candidate numbers to test: 11, 22, 33, 44, 55, 66, 77, 88, 99–all palindromes which don’t change by reversing their digits.

Here are the resulting sequences:







77→49→36→18→8 BINGO!! That’s a long sequence of five numbers!



My secret number is 77, and if I mention that it equals my house number multiplied by the total number of letters in SECRETS, then you can also deduce that my house number is 11–the same as the number of today’s blog post!


The clearest and basically forced win for Black is 1…d3 2 Qxe4 (or 2 Qc1 d2! 3 Qxd2 Qb1+) 2…Bxe4 3 Kf1 d2 4 Ke2 Bd3+! (the key tactical point) 5 Kxd3 d1=Q+ or 5 Kxd2 Bxb5, with a decisive material advantage.


In this second chess puzzle, White wins most clearly with 1 Qg5! dxe5 (or 1…Qxe5 2 Qxe5 dxe5 3 g5, after which Black will lose his knight or his bishop) 2 Ne4 (2 Rxd7 is also very good, but 2 Ne4 is even simpler) 2…Raf8 3 Nxf6 Rxf6 4 Rxd7 Qxd7 5 Qxf6+. Again, the material advantage is totally decisive. With the benefit of hindsight from his disaster, Black would have had to try 1…Nd5, but of course White should still win after 2 Qxe7 Nxe7 3 exd6.

To finish this article, you can, by clicking on the following hyperlinked photo, enjoy a short video featuring several stars. They include one of my favourite actresses, the lovely Teresa Palmer. There’s a great song too, of course, and I presume you’ve already guessed its title…“Secrets”!

Click on the photo to see a very short and good music video.

“The face is the mirror of the mind, and eyes without speaking confess the secrets of the heart”–St. Jerome.



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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