Blog Post #7: Gifted

Dear Readers,

Yesterday, I wrote a full article from my heart as a gentle tribute to a wonderful lady and dear friend who died last Thursday. My small tribute may appear here soon, but only with the clear approval of the lady’s family, and that is why I am not publishing without asking.

Also within the past few days, my wife, Jenny, and I saw a very thought-provoking new film called “Gifted”. Afterwards, Jenny and I talked about how a 7-year-old girl with the ability to mentally calculate 57×135 in a matter of seconds was certainly extremely “gifted”, but it’s also very worthwhile to consider that we are all greatly gifted by God having given us each other and one lifetime now in which to give as much love as possible while we still can. My friend who passed away always made an incredible difference in the lives of thousands of children and adults through her great kindness.


Our good word challenge is to start with GIFT and, by changing only one letter at a time, get to LOVE in 4 steps. At each stage, we must always still have a proper English word.


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Mary was the 7-year-old Math genius in “Gifted”. In schools where I have worked, students were always warmly encouraged to try to discover different, interesting ways of solving problems. Can you think of some ways of very quickly calculating 57×135 mentally, as Mary did?



What happened to the plant in the Math class?

It grew square roots!



It’s White to play and, even without the pawn on d4, there would still be a forced checkmate in not more than 4 moves. Have fun solving the puzzle!


For personal reasons, I know that I may not be publishing any more articles until August. So, here comes an original, super-sizzling, summer brainteaser to keep some readers thinking for a good chunk of July…unless you’re like Mary and are able to solve it all in a few seconds!

Jenny has thought of a very particular two-digit whole number. She tells it to Paul. Paul has himself thought of a higher two-digit whole number. He then announces, “The sum of all the whole numbers that are actually smaller than Jenny’s number is exactly equal to the sum of all the whole numbers that are bigger than Jenny’s number but are not actually bigger than my number.”

Your brainteaser challenge is to figure out precisely what two-digit number Jenny thought of, and also precisely what two-digit number Paul thought of.

Hint: To illustrate the meaning, if Jenny’s and Paul’s numbers had been one-digit numbers (instead of two-digit numbers), then Jenny’s number would have to be 6 and Paul’s number would have to be 8. That’s because 0+1+2+3+4+5=7+8 is the only “one digit” solution that meets all the requirements. Can you find the harder “two-digit” solution?



One solution is GIFT→LIFT→LIFE→LIVE→LOVE, but you may have thought of other ways.


While watching the film “Gifted”, I quickly calculated 57×135 by realising that it is equivalent to 19×405. (I divided 57 by my favourite number 3 to get 19, and to keep the balance I multiplied 135 by 3 to get 405.) Now, 19×405 is equal to 20×405-405. I know that 2×405=810, and so 20×405=8100. Then, 8100-405=7695. Of course, there are many other perfectly good ways of tackling that problem.


The position occurred in Tosic vs. Marcetic, Serbia 2012. White forces checkmate with: 1 Rb7+ Ka8 2 Rb6! Bd3 3 Bxd3 Rxd3 4 Ra6#.


The solution will be given next month, early in August. (Update: The solution is given in Blog Post #10, published on 2 August 2017.)

I would like to finish this article by wishing you a wonderful month of July, and I will say a gentle goodbye for now by leaving you with these words from Saint Mother Teresa: “Kind words can be short and easy to speak, but their echoes are endless.”

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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