Blog Post #39: Sharing

Dear Readers,

It is always a great pleasure for me to discuss rich and beautiful subjects such as Chess and Mathematics with other avid readers and friends who are similarly happy to share good thoughts.


Two days ago, my family and I enjoyed a lovely meal and chat with David, a long-time friend of ours who is a talented chess player and puzzle solver. Following now is a dose of sneaky puzzles for you and David to have fun with.


Remove just one letter from DAVID so that the remaining four letters–read from either left to right or from right to left–make proper English words.


The multiplication chart shows the results

1, 2, …,12; 2, 4,…,24; …;11, 22,…,132; 12, 24,..,144


1×1, 1×2,…,1×12; 2×1, 2×2,…,2×12; …; 11×1, 11×2, …,11×12; 12×1, 12×2,…,12×12.

Can you think of a quick way of figuring out (without needing a calculator) the sum total of all the one hundred and forty-four results:

1+2+…+12+2+4+…24+…+11+22+…132+12+24+…+144 ?


The given position is based on a famous chess game from 1961 between two of the-then strongest players in the world.

White has an invisible knight somewhere on the f-file.

  1. Where should the white knight be so that White (to move) can force checkmate in only two moves?
  2. Where should the white knight be so that White (to move) can force checkmate in only three moves?


An elderly couple in a restaurant ordered one cheeseburger, one portion of fries and one drink. When the old couple sat down, a minister sitting near them observed the old man cutting the burger in half, taking half of the fries and giving his wife half, and pouring half of the drink into the extra cup he had requested.

The minister was puzzled, so he went over and kindly said to the couple that if they couldn’t afford a meal each, he would be more than happy to pay for them. The old man shook his head and told him that there was no need because he and his wife had shared everything for the past 50 years.

The minister went back to his seat and then he saw the old man eating while the old woman just sat there doing nothing.

He went over to them again and asked the old lady why she wasn’t eating. She said, “Well, it’s his turn to use the teeth!”



By removing the first D from DAVID, we see AVID from left to right or DIVA from right to left.











  1. If White has an invisible knight on f8, then he forces checkmate with 1 Qh7+ Kxf8 and then either 2 Qh8# or 2 Qxg7# or 2 fxg7#.
  2. If White has an invisible knight on f4, then he forces checkmate with 1 Qg6!! fxg6 2 Rxg7+ and 3 Nxg6#.


An excellent quote from Philippians 2:3-4 in the Bible is:

“In humility, value others above yourselves, not looking to your own interests, but each of you to the interests of the others.”

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 #39: Sharing”

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