Blog Post #6: Kindness

Dear Readers,

One of my favourite Japanese proverbs is: “One kind word can warm three winter months.” So, a full and really thoughtful letter today from a very kind Scottish friend named Elaine will honestly probably help me for the rest of my life!

In addition to her kindness, another of Elaine’s great sources of strength is her faith, which has helped her to stay happy and positive throughout all of life’s challenges. So, the following reflection from Pope Francis is for Elaine and for everyone who would like to use it well themselves and to pass on to others. “There are difficult moments in life, but with hope the soul goes forward and looks ahead to what awaits us”–Pope Francis.


You might be wondering…did he misspell Elaine?! In fact, Elaine already had her birthday, on 27 June, but Eliane (the wife of a teacher colleague of mine) has her birthday 11 days later. In how many days (from 5 July, as I write now) will Eliane have her birthday?


One of Eliane’s sons was recently wearing a truly terrific T-shirt designed by Tuli, Spirit of Africa. On it was a lovely 5 by 5 square array of four-legged animals. How many legs were there on the animals altogether?


My initials are PM, for Paul Motwani. For simplicity, just suppose that everyone has two letters from the English alphabet for their initials. In that case, how many different possibilities would there be?




Today, I wished a very happy birthday to two different friends on Facebook. Curiously, they both have initials in which the two letters are the same (e.g. AA or BB or CC, and so on), though those two friends do not actually have the same initials as each other. Alphabetically, the male friend’s initials happen to come somewhere before the female friend’s initials. Imagine that you were to list all the possibilities for their combined initials like AABB, AACC,…, and so on, in alphabetical order. How many possibilities would there be altogether?


Guess how a Scottish mathematician proved that he was generous, cultured, and good at English too…!

He said, “I’m taking my wife to something special beginning with b, and it rhymes with wallet!”


The wallet is – – – – – – – than the – – – – – – –. Which seven-letter English word could fit in both of the “blanks” to make a sensible sentence? The spelling should be identical in both “blanks”.


White is far ahead on material, but that will be of no help because what matters much more is that his king is in a perilous position. It is Black to move and force checkmate in not more than 4 moves (meaning four by Black, starting now, and three by White as the players of course take alternating turns).



As Eliane’s birthday comes 11 days after Elaine’s birthday on 27 June, it’s going to be on 8 July, just 3 days from today (5 July 2017, as I write now).


The total number of animal legs is 5x5x4, making a perfect 100.


Using English alphabet letters only, we would have 26 choices for a person’s first initial. In all 26 of those cases, we would have 26 corresponding choices for the second initial. Therefore, the total number of choices is 26×26, which gives 676 possibilities.


According to the information given in puzzle, the combined initials of the two friends in alphabetical order could be:

AABB; AACC;…; AAZZ (25 possibilities there)

BBCC; BBDD;…; BBZZ (24 possibilities there)

XXYY; XXZZ (2 possibilities there)

YYZZ (1 possibility there).

The total number of different possibilities is 1+2+…+24+25.

One sneaky way of figuring out that sum quickly is to write it as 0+1+2+…+23+24+25. Then we have a sum of 26 numbers, and we can group the numbers into 13 pairs which each have a mini sum of 25: (0+25)+(1+24)+(2+23)+…+(12+13). The grand total is therefore 13×25, which makes 325.

(For the record, my birthday friends’ combined initials are actually HHSS for Harry H. and Sarah S.)


Actually, I may be taking my wife to a ballet, and you’ll be relieved to hear that I know it doesn’t rhyme with wallet!!


One possible solution is certainly THE WALLET IS LIGHTER THAN THE LIGHTER.


The position occurred in Povorotov vs. Belozerov, Kazakhstan 2012. Black can quickly force checkmate against White’s exposed king with: 1…e5+! 2 Kxe5 Re8+ 3 Kd4 (or 3 Kd6 Qc6#) 3…Qe3+ 4 Kd5 Qe5#.

I’ll conclude today’s article with the following quote: “Kindness spreads so quickly, you couldn’t stop it even if you tried!”–Sian E. Morgan.

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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