Thinking back more than 40 years to my high-school days in Dundee, Scotland, one of my jolly friends there was nicknamed ‘Happy’, and that’s exactly how he has always been to me and, I believe, to everyone who knows him. I received a very kind message from ‘Happy’ last month when I turned 60, and he sent another lovely message to wish Jenny and myself a happy 27th wedding anniversary yesterday ♥😊😊♥
One of my favourite, beautiful word facts is that I was born makes rainbows, and now I like to think of S.M.I.L.E.S. as standing for Sixty May I Love Everyone Sincerely. A couple of my favourite sayings are, “If you see someone without a smile, give them one of yours” and “Your smile is a signature of God on your face.”
Smiles could be seen everywhere at Musica Mundi School last week, as the leaders, teachers, staff, students, parents and many other dedicated supporters helped the school to complete its fourth wonderful year, so far.
I have a fresh puzzle for you, inspired by the nice photo below…
Imagine that the four of us in the photo are thinking of positive whole numbers with the following special properties:-
The two ladies are thinking of the same number as each other;
the student is thinking of the largest number of any of us;
my number is the exact average (or ‘arithmetic mean’) of all of our numbers;
and now the most revealing, key fact: the sum obtained by adding up the four numbers exactly equals the product obtained by multiplying the four numbers together!
Your fun challenge is to figure out exactly what numbers each of the four of us must be thinking of to fit the wee ‘Maths st😊ry’.
The magical photo below by Erika Sziva encourages good, deep thinking…
In between my 60th birthday and 27th wedding anniversary, Jenny and I went for a weekend to celebrate with friends living in a Dutch village with the perfect name: it’s called Best! Our dear friends there are literally NEAR, as their names are Nico, Erika, Alex & Robert 😊😊😊😊
Nico gave me a T-shirt with some amazingly creative mathematical expressions printed on it!
Erika and Robert now have two terrific chess sites. Their first one is http://www.debestezet.nl
and, since February 2022, they’re also running http://www.raindroptime.com.
Robert and Erika’s sites are a treasure trove for chess boards, pieces, books, computers, software and delightful gift items such as chess socks, T-shirts, ties, cufflinks, pin badges, bracelets, keyrings and USB storage in the form of a chess king. You’ll also find some goodies relating to the game of draughts. Robert (an IT expert) & Erika (a WGM=Woman Chess Grandmaster) are renowned for their very fast, efficient and friendly service.
Let’s round off this article with a lovely chess puzzle.
The most important thing I have learned in my life is that God loves us all.
I wish you a very happy day now.
Paul M😊twani ♥ xxx
P.S. = Puzzle Solutions
In the number puzzle, 1 + 1 + 2 + 4 = 8 = 1 x 1 x 2 x 4.
The ladies thought of 1; the student thought of 4; I thought of 2.
In the chess puzzle, white’s invisible knight is NOT on c5, because then checkmate could be forced too quickly with 1 Qe6+ Ke8 2 Qg8#;
rather, the invisible knight is on g7, which leads to