Dear Readers,
I am delighted to have won the British Senior (Over 50) Chess Championship jointly with Chris Duncan and Philip Crocker at the Riviera International Centre in Torquay.
Dear Readers,
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
Dear Readers,
My wife, Jenny, and I look forward to celebrating our wedding anniversary number 33 next month and, before then, in just 3 days from now, Jenny is due to have her birthday number 33 x 2. Here are 3 of ‘my Queen’s’ favourite photos from the past few days…
Here in Blog Post #128 on my 60th birthday, I would like to include a wee puzzle involving the number 128, also because H.R.H. Queen Elizabeth II has now been the wonderful queen of the United Kingdom of Great Britain and Northern Ireland for a remarkable 70 years & 128 days, so far!
The numbers puzzle is this: use 1, 2 and 8 just once each in a calculation that results in the number 128. You can freely use any of +, -, x, ÷, parentheses ( ), and exponents wherever you wish.
As the Queen is the most powerful piece in a game of chess, let’s have a beautiful chess puzzle in which it’s White to play and force a win in just 3 moves, and White’s queen plays a stunning role…
Today at Musica Mundi School where I work, three of the graduating senior students gave fascinating presentations detailing the tremendous research that they had done as part of the very high-level Musica Mundi School Diploma. Warm congratulations to all of them, and to the further four students who will present tomorrow morning.
With kindest wishes as always,
Paul M😊twani xxx ♥
P.S. = Puzzle Solutions!
2(8-1)=128 in the numbers puzzle.
In the chess puzzle, White wins with 1. Ne6+!! because of 1…fxe6 2 Qf8# or 1…K retreats 2. Qb8+ or 1…Qxe6 2 Qh6+!! intending 2…Kg8 3 Qf8# or 2…Kxh6 3 Bf8#, a lovely finish ♥😊♥.
Dear Readers,
I would like to begin by offering, with most sincere sympathy, kind thoughts and prayers for Rooney, a friend whose sister, Gina, passed on a couple of days ago. I know (from similar personal experiences involving loved ones) that God can grant us gentle comfort through positive, happy memories of the precious times shared with people so close to us. I also believe that we will meet again later in a perfect place that God has prepared for us.
Knowing the lovely tradition of dedicating the month of May to Our Lady, Mary, this is a perfect time to recall the following prayer:
Dear Readers,
My family and I would like to wish everyone a very happy Easter and, particularly for young Super Sigurd, a really happy birthday today, too ♥
Vilja, Ask-Johannes and Sigurd all love puzzles, and today we’ve got a full feast for them ♥
SUPER Word Puzzle!
‘SUPER’ is quite a special word because if we repeat any one of its five letters, we can, in each case, rearrange the resulting letters to make proper six-letter English words.
For example, SUPERR can be rearranged to make PURSER.
Your fun word puzzle is to rearrange each of
SUPERS
SUPERU
SUPERP
&
SUPERE
to make proper six-letter English words.
SUPER Number Puzzles!!
The number puzzles will involve a special focus on the decimal number 14.4, in honour of Super Sigurd’s birthday on 14 April today ♥
Let’s also quickly check, here in Blog Post #125, that everyone is comfortable with the mathematical meanings of ‘cube root’ and ‘square root’.
The square root of 25 is 5 because 5 x 5 = 25.
The cube root of 125 is 5 because 5 x 5 x 5 = 125.
2. I am now thinking of another specific whole number, S. It’s the last two digits of the year in which Super Sigurd was born. Remarkably, the square root of (14.4 x S) is the new age that Sigurd is on his birthday today! Exactly what number is S ?
SUPER Chess Puzzle!
As Sigurd’s favourite number is 4, enjoy solving the following chess puzzle in which it’s White to play and force checkmate in 4 moves.
I will round off by again wishing everyone a very happy Easter ♥♥♥
With kindest wishes as always,
Paul Motwani xxx
P.S. = Puzzle Solutions!
SUPERS→PURSES
SUPERU→PURSUE
SUPERP→SUPPER or UPPERS
SUPERE→PERUSE, PUREES or RUPEES
In the chess puzzle, White forces mate with 1 Rxe8+ Kh7 2 h5! gxh5 3 g6+ Kh6 4 Rh8#.
If Black instead promotes either the c-pawn or the d-pawn at move 2 in the line given above, then White responds with 3 hxg6#, checkmate!
Dear Readers,
I wanted to share a couple of Bible verses which are short yet remain always extremely important and helpful.
During her life on Earth, my mother’s many very precious gifts to me included two books about Mother Teresa of Calcutta (1910-1997), who was canonised as St. Teresa of Calcutta in 2016. The following image is one of my absolute favourites.
For me, the peacefulness and beauty that I also find in puzzles featuring Chess, Mathematics or gentle words, for example, make them all interesting and appealing, too.
A GOOD WORD PUZZLE
From the word GENTLE, remove two letters which are a standard abbreviation for ‘for example’. Use the remaining four letters to make a proper 4-letter English word which is timely now.
A BEAUTIFUL NUMBERS PUZZLE
To celebrate the birthday today of Natasha, a friend of mine, I offer this puzzle here in Blog Post #124: If I calculate the sum of Natasha’s new age now and her age n years ago, then multiply by n, the final result is 124.
What is Natasha’s age now, and what is the value of the whole number n?
A WONDERFUL CHESS PUZZLE FROM AUSTRIA ♥
A FUN MIND-READING PUZZLE!!
I am imagining five Queen Anne’s…
Anne I
Anne II
Anne III
Anne IV
Anne V
Which particular one holds the key to where the Musica Mundi School leaders and students have gone on a 4-day school trip?
Wishing everyone more peace and love,
Paul Motwani xxx
P.S. = Puzzle Solutions!
Dear Readers,
As a nice, wee warm-up challenge, rearrange the letters of the plural word ‘LAMPS’ to make a singular word. Congratulations for getting ‘PSALM’, and you may like to know that that little puzzle–and indeed this article–was inspired by the beautiful Bible Psalm 119:105 “Your Word is a lamp to guide my feet and a light for my path.” No matter what answers I might be looking for, they are always to be found in God’s perfect Word within The Bible.
I am due to turn 60 later this year, while one of my sisters has her birthday today. What total should we get if we add her new age now to the two-digit number located at the end of the (four-digit) year when she was born?
You could rightly assume that my sister was born in a 20th century year and then, no matter which year I mean, its two-digit end part + my sister’s age now will always give 122, perfect for today’s blog post 😊.
Have fun solving it…before checking answers…
just down below!
Black wins with 1…Qxf2+ 2 Kh1 Qg1# or
White wins with 1 Rf7+ Kg8 2 Re7+! K moves 3 Rcxe8#, checkmate!
I would like to round off now by wishing everyone a very happy weekend.
With kindest wishes as always,
Paul M😊twani xxx
Dear Readers,
Many years ago, during a show within the theatre of my previous school, the delightful song ‘Three is a Magic Number’ started playing, and suddenly hundreds of smiling people looked directly at me because practically everyone there knew that 3 is my absolute favourite number! (A new version of the song plays near the end of ‘Spiderman: No Way Home’.)
I might have been thinking about it less often when I was a child…
…but now there are honestly lots of reasons for my love of three, and the following lovely pictures do show some of them:-
Another favourite photo is the following stunning view of the French Alps that people shared via Facebook recently.
My current house number is 11. Three fun facts involving it are:-
11 squared = 121, the palindromic number of this particular blog post
121 is the smallest 3-digit number which has exactly three factors: 1, 11 and 121; that happens because it’s the square of a prime number
11 cubed (or 11 raised to the power of 3) equals 1331,
another pretty palindrome 😊😊😊
It’s time for a quick, wee word puzzle… Rearrange the letters of TURN THE KEY to make THEN + the six-letter name of a beautiful country.
The beautiful Musica Mundi School (where I work as the Mathematics Teacher) is currently blessed with 7 lovely Turkish students. One of them is Cansu, who easily solved a little Christmas puzzle that kind friends first shared with me before I shared it with others, too.
My youngest, 15-year-old niece (in England) and my cousin Anne (in Scotland) both thought of moving number 9 to the first tree, after which the sum of the numbers on each tree will be exactly 15.
Cansu no less creatively thought of just moving 8 to the first tree, after which the individual tree sums would come to 14, 15 and 16, forming a nice sequence of consecutive numbers.
Now imagine that we wanted to have more than three trees. We’ll still be using the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 just once each.
How can the numbers be distributed such that the total on each tree is equal, using as many trees as possible?
Still thinking about my colleagues and my students, I would like to wish very bright ☼ happy birthdays to Norea (for this past Thursday), Mila (yesterday), Andrea (today) and Headmaster Herman for tomorrow ♥.
I know lots of people who love a good chess puzzle, and so let’s enjoy the following…
I would like to conclude now by wishing everyone a very blessed, joyful Christmas and a happy new year coming soon, too.
With kindest wishes as always,
Paul M😊twani xxx
P.S. In the chess puzzle, White’s invisible pawn is on f3, and Black forces checkmate with 1…Rf4+! 2 gxf4 Qh4+ 3 Kf5 Qxf4#, a beautiful finish!
In the ‘maximum number of trees’ puzzle, the answer is to have five trees with these numbers on them: 1 & 8; 2 & 7; 3 & 6; 4 & 5; 9. In that way, the total sum on each tree equals nine.
Dear Friends,
Have you ever loved someone so much that you could feel your heart overflowing, and have you wished for someone special to love you as much as that? The joyful truth is that we are all loved infinitely more than any of us can really imagine fully.
We are loved completely, totally and perfectly by God. That is by far the most happy and important thing that I know, for sure. Indeed, I am glad to declare honestly that I am more sure about God’s love for us than I am about anything else, including everything regarding Chess, Mathematics and other subjects that I have studied practically every day for decades.
My biggest Christmas wish is for as many people as possible–everyone, really–to live the rest of their lives joyfully knowing that God loves them, and that He has prepared a magnificent home for us in His Kingdom.
I could have stopped just above, for the most important things have been said…
…but I would like to also offer some personal thoughts for several dear friends.
Firstly, for two distinguished gentlemen who are brothers and whose father is ill, I am thinking of your whole family with kindest thoughts and prayers. I would also still like to most sincerely wish the older brother a happy birthday coming in five days from now, five days before Christmas.
A super-bright ray of sunshine comes to mind as I think of some other lovely friends who are now back living in a country for which the six-letter name can be made using all the letters of RAY NOW 😊.
Congratulations for getting NORWAY 😊.
In Norway, they of course have lots of SNOW even when it’s not Christmas!!
OK, you’re quite possibly asking, “What do you mean by A*(100-A)?”
Well, Ask-Johannes (the boy beside his sister in the photo below) sent me a note of his favourite whole number (let’s call it A), and A*(100-A) gives a year as early as possible in the 20th century (but not 1900 or 1901, for example, because we couldn’t get those results from A*(100-A)…
Really well done if you have already figured out Ask-Johannes’ favourite whole number, A.
In case you might be pondering the matter a little more, you can see that smiling Sigurd August wants to offer a helping hand! So, let’s now introduce his own favourite whole number, S…
Given what has already been told, if I also tell you that S*(A+1) = 300, then you could now know the precise values of A and of S.
OK, let’s bring ourselves right up to date by revealing that A=74 and S=4.
Check: 74*(100-74)=1924, quite early in the 20th century, and 4*(74+1)=300, as required.
Princess Vilja is so kind that she’ll surely forgive me for keeping her waiting a wee bit by not using the good rule of ‘ladies before gentlemen’ on this occasion. I do use it almost every day when queueing for lunch at the beautiful Musica Mundi School; I like for ladies and girls to go before me in the line, even if the ‘queue’ is mostly pretty short.
Today, though, already knowing Vilja’s brothers’ favourite numbers (4 and 74) will enable you to easily figure out Princess Vilja’s favourite number in a moment…That’s because not only does Vilja’s favourite whole number, V, equal the total of her mum’s two favourite whole numbers, Y1 and Y2, but also A + S + V + Y1 + Y2 = 100 exactly!
Now we also know that the sum of Y1 and Y2 is 11 because V=11, but what exactly are Yngvild’s favourite two numbers, Y1 and Y2?
I will simply announce directly that Y1=3 and Y2=8, because we still have a special, quite remarkable, surprise in store for the lovely Norwegian friends…
As this is Blog Post #120, let’s make a set of four numbers 1, 3, 8 and 120 for my 1st friends in Kolbotn. I’m going to say, “Pick any two different numbers from 1, 3, 8 and 120. Multiply the two numbers together. Now add 1, because you’re all #1 in God’s eyes.”
The above sequence of steps could have given you any of these six possible results:
1 x 3 + 1 = 4
1 x 8 + 1 = 9
1 x 120 + 1 = 121
3 x 8 + 1 = 25
3 x 120 + 1 = 361
8 x 120 + 1 = 961.
The remarkable thing is that every single one of those results is a perfect square number!
4=2 squared; 9=3 squared; 121=11 squared; 25=5 squared; 361=19 squared; 961=31 squared 😊
Since Vilja, Ask-Johannes and Sigurd August all enjoy chess, let’s conclude with a position in which it’s White to play and force checkmate in just 3 moves.
I wish everyone a very happy Christmas and New Year coming soon.
With love and kindest wishes,
Paul M😊twani xxx
P.S. Well done for finding the chess solution 1 Nf6+! Kf8 (or 1…Kh8 2 g7# or 1…Bxf6 2 Re8#) 2 g7+ Kf7 3 g8=Q#, checkmate!
P.P.S. I also want to most sincerely wish a happy birthday tomorrow to another Norwegian friend whom I am often thinking of, too ♥
Dear Readers,
A friend of mine once asked me if I had an absolute favourite word. Though I was not expecting her question, I could answer almost immediately with “Love” because God is Love and, when people are kind and loving to each other, God’s love spreads in infinitely many good ways to touch more hearts.
Two of my favourite short Bible passages are:
“Be imitators of God, as beloved children.”—Ephesians 5:1
“Train up a child in the way he should go; even when he is old he will not depart from it.”—Proverbs 22:6.
Of the many thousands of people whom I know, and billions whom I don’t yet know, everyone should matter to everyone. They should all be SP_ _ _ _ _ .
Please know that YOU ARE SP; y😊u’re truly SPECIAL.
Early this morning via Facebook, I wished very happy birthdays to Danielle and to Stevie, two of my friends there. Today is of course also the birthday of lots and lots of other people, including World Chess Champion Magnus Carlsen. Everyone is wished a wonderful day, and for Magnus a great game #4 in his current World Championship match with Ian Nepomniachtchi in Dubai.
Maybe your birthday is coming during the month of December…and if so, let’s say that your Big Birthday is on day number B (e.g. B=either 1, 2, 3,…, 30 or 31) in December…then TODAY is the only day in the whole year when I or anyone can actually wish you a super-happy birthday exactly B days early before December B 😊.
Whenever your birthday is, I want right now to wish a lovely HAPPY BIRTHDAY FOR YOU. Good reasons for doing it today, without delay, are that I’m here and able to do it now, and also (I couldn’t resist this one…) HAPPY BIRTHDAY (13 letters) x FOR (3 letters) x YOU (3 letters) is nice because 13 x 3 x 3 = 117 here in Blog Post #117 😊.
I will round off with a wee selection of beautiful ‘happy memory’ photos. Each one is, in its own way, a good reminder to me of ‘Love Like A Child’.
With love and kindest wishes as always,
Paul M😊twani xxx
Paul Motwani 