Blog Post #23: Neighbors

Dear Readers,

One night recently, my wife and son and I drove from Belgium to the nearest place beginning with A, but just among cities shown on the little map picture. The next day, we flew to the most southerly place beginning with S, again just among those indicated on the little map below.

In Amsterdam and in Sicily, we greatly appreciated having a very pleasant and peaceful time with everyone whom we met. I am happy to report that we witnessed no eruptions at all!


Rearrange the letters of NEAT to make the name of a famous volcano.

Times and distances are really not big or important obstacles to overcome;

rather, we should reflect and focus more on being kind to our neighbors wherever we are.


The wordsearch below includes the fun challenge of finding some of the good words and qualities which are often referred to as the ‘Fruits Of The Holy Spirit’.

Siblings and friends who love each other well will be able to love other people too.


In a certain family, there were equal numbers of male and female siblings. Each person was asked to calculate his or her number of brothers divided by his or her number of sisters. It turned out that half the people got one answer, while the other half got a bigger answer which was a whole number times the smaller answer. Your brainteaser is to figure out exactly how many siblings there were. There is a unique proper solution, with no funny tricks!


Who listens well to both sides of a quarrel…?

The next-door neighbors!


I’m using my own initials in a new way here to have some sneaky fun with Pinocchio, Archimedes (of Syracuse in Sicily) and Math!

Archimedes’ favourite personal mathematical discovery was that the volume and the surface area of a sphere inscribed in a cylinder of the same height and width are exactly two thirds of the respective volume and surface area of the cylinder. (See also Blog Post #79: For Elizabeta!)


If we were to be told the volume of the blue sphere shown above, what would be the quickest way to figure out the left-over volume within the cylinder?


Suppose that two giant beefburgers together cost a whole number of euros, but seven giant beefburgers cost more than 100 euros. There is no special discount (or surcharge!) for buying multiple beefburgers. What is the minimum possible price of each giant beefburger?


In Sicily, I read some of “The New Sicilian Dragon”, a highly entertaining Everyman Chess book from 2009 authored by Grandmaster Simon Williams, who is affectionately known to many as the ‘Ginger GM’.

I also enjoyed listening to Simon’s commentary on some blitz chess games between superstars Hikaru Nakamura and Fabiano Caruana. Here is one position which arose.

It is White to move, but his bishop is pinned. With best play now, is White winning or is he losing or is he drawing?



NEAT rearranges to make ETNA.



There were 4 siblings: 2 male & 2 female. The ‘boys’ each have 1 brother and 2 sisters; they’ll calculate ½. The ‘girls’ each have 2 brothers and 1 sister; they’ll calculate 2/1, which equals 2. Note that 2 is 4 times bigger than ½.


Since the sphere occupies two thirds of the cylinder, the left-over volume is one third of the cylinder. 1/3 is half of 2/3, so simply halving the volume of the sphere gives us the left-over volume.


The minimum giant beefburger price is 14.50 euros. That fulfils the conditions that two beefburgers together cost a whole number of euros, and seven beefburgers cost more than 100 euros.

P.S. I’m not a beer drinker!!


The super-strong move 1 Qa3!! wins, and it actually induced Black to resign in the game. If 1…Qxf1+ 2 Kh2, then Black has no good way to defend his e7-pawn, and after it falls his king and rook will be in king-sized double trouble!!

As it’s now less than 7 weeks until Christmas, I’ll finish with this powerful yet peaceful picture & link: Please enjoy beautiful Vangelis music via the link, 13mins 4secs.

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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