Blog Post #13: Differences

Dear Readers,

I once challenged a student to mentally rearrange the letters of C IN DETAIL to make a proper nine-letter English word. As a bonus clue, I said, “The number of C IN DETAIL people is zero”! Can you also now figure out the details mentally?

Though God made us all special and unique–never exactly the same as anyone else–I believe that we will have succeeded in finding a perfect, IDENTICAL answer! Naturally, our differences need not actually cause us any insurmountable problems in life, if we remember to peacefully accept each other. A very helpful and inspiring quote is: “Have a big enough heart to love unconditionally, and a broad enough mind to embrace the differences that make each of us unique”–D.B.Harrop.

I have two nieces and one nephew who are all wonderfully different. I can tell you that the age difference between the youngest one and the “middle” one is the same as the age difference between the “middle” one and the oldest one. How many of their ages would I need to tell you so that it would be possible to figure out the total of the three ages?


White (to move) has a winning position, and there are undoubtedly different ways to win. However, can you find an absolutely forced route to victory in which every move by White, up to and including checkmate at the end, puts Black in check?


How could you tell that I’m a mathematician–and not a farmer!–when my farmer friend asked me to help him round up 27 animals…?

…I said, “30”!


Within the next few days, two of my good friends, Erik and Christine, have their birthdays on consecutive days in August–Erik first. If I were to multiply Erik’s day number by Christine’s day number, the result would end with a digit 6 on the right. When is Erik’s birthday, and when is Christine’s birthday?

Now for two other special friends…! Micky has the same birthday as Christine, whereas Nicola’s birthday will be sooner. When is Nicola’s birthday, if I tell you that the product of her day number and Micky’s day number would end with a digit zero on the right?

In case your birthday is also coming soon, I wish you a wonderful time, too!


Throughout several decades, from a time when I was very young, I have liked many great songs by the famous Norwegian band, A-HA.

One of my absolute favourite songs by them is called “Differences”, and here is a good link to them performing the song at a 2001 Nobel Peace Prize concert.

Here also is a link to another beautiful A-HA song called “Solace”.



You would only need to be given the age of the “middle” child. Then the total will simply be three times that age. For example, if the three ages were 10, 14 and 18 years, then the total would be 42 years, the same as 3×14 years. That works because there is a common difference between the numbers: 18-14=4 and 14-10=4, too.


White wins quickly by force with 1 Nf6+ Kh8 (or 1…Kg7 2 Nh5++ followed by 3 Qg7#) 2 Ng4+!! Nxd4 (there is nothing better) 3 Bf6+ Kg8 4 Nh6#, checkmate!


The birthdays are as follows:-

Nicola: 25 August;

Erik: 27 August;

Christine & Micky: 28 August.

The Erik-Christine product ends with a 6 because 7×8=56.

The Nicola-Micky product ends with a 0 because 5×8=40.

I will finish this article with a good quote: “Share our similarities, celebrate our differences”–M. Scott Peck.

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.

2 thoughts on “Blog Post #13: Differences”

    1. Dear Stefan,
      Thank you for your kind message, which is greatly appreciated. I am very glad that you are enjoying the blog.
      Yesterday, I watched the exciting rapid-play tie-break games between Etienne Bacrot and Laurent Fressinet to decide the French Chess Championship. It was a terrific battle!
      Many thanks again for keeping in touch.
      With all best wishes, Paul.


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