Blog Post #146: Three Books πŸ˜Šβ™₯😊

Dear Readers,

Out of the many millions of books that have ever been written, if I had to pick just 3–my absolute favourite number!–of them to keep enjoying forever, then my top selection would probably be the following:-

  1. The Holy Bible, because it’s a perfect book revealing to us the Word of God, which can be trusted totally and is of supreme importance.
My selected text today is: Jesus said, “I am the way, the truth, and the life. No one comes to the Father except through me.”-John 14:6 β™₯

2. After my clear first choice above, it’s not at all easy for me to pick a second book in preference to all other books, but I’m sure that a very strong candidate would be: ’15 Minutes Alone With God’ by Bob Barnes.

Though the book has the subtitle ‘For Men’, every page has wonderful reflections for everyone.
Here is a short extract from page 9 of my copy: “Time with your heavenly Father is never wasted. If you spend time alone with God in the morning, you’ll start your day refreshed and ready for whatever comes your way. If you spend time alone with Him in the evening, you’ll go to sleep relaxed, resting in His care, and wake up ready for a new day to serve Him.” β™₯

If I fast-forward to pages 185-188 of the book, there’s a four-page article entitled I Didn’t Believe It Anyway, which includes the following powerful poem:

‘Twas the night before Jesus came and all through the house

Not a creature was praying, not one in the house.

Their Bibles were lain on the shelf without care

In hopes that Jesus would not come there.

The children were dressing to crawl into bed,

Not once ever kneeling or bowing a head.

And Mom in her rocker and baby on her lap

Was watching the Late Show while I took a nap.

When out of the East there arose such a clatter,

I sprang to my feet to see what was the matter.

Away to the window I flew like a flash

Tore open the shutters and threw up the sash!

When what to my wondering eyes should appear

But angels proclaiming that Jesus was here.

With a light like the sun sending forth a bright ray

I knew in a moment this must be THE DAY!

The light of His face made me cover my head.

It was Jesus! Returning just like He had said.

And though I possessed worldly wisdom and wealth,

I cried when I saw Him in spite of myself.

In the Book of Life which He held in His hand

Was written the name of every saved man.

He spoke not a word as He searched for my name;

When He said, “It’s not here,” my head hung in shame.

The people whose names had been written with love

He gathered to take to His Father above.

With those who were ready He rose without a sound

While all the rest were left standing around.

I fell to my knees, but it was too late;

I had waited too long and thus sealed my fate.

I stood and I cried as they rose out of sight;

Oh, if only I had been ready tonight.

In the words of this poem the meaning is clear;

The coming of Jesus is drawing near.

There’s only one life and when comes the last call

We’ll find that the Bible was true after all!

3. No further book is really needed, but still I thank God every day for having let me enjoy many thousands of fascinating puzzles in my life so far. For me, a compilation of all those puzzles, about Chess, Mathematics, Words and more, would certainly be a treat! I believe that the puzzles in store in Heaven will be better and more magical than I can possibly imagine. For the moment, I can only offer what I know right now. So, I would like to share some surprises with you, since God gives us good thoughts to be shared. Here comes fresh puzzle ideas that came yesterday evening and in the morning today…with some extra bonuses this evening!

I would like to specially dedicate the puzzles to my excellent colleague Jens Van Steerteghem, his brother Nick, and their father Eric, as all three gentlemen are passionate about puzzles and have great talent for solving them!

Get ready for a race…but first rearrange the letters of TIME RAN
to make a seven-letter female first name, the nice name of Jens & Nick’s mother
A wee clue is that her name begins with MA, and it’s a very popular name in Belgium 😊.


The name ‘Eric’ always makes me think of the famous missionary Eric Liddell–affectionately known as ‘The Flying Scotsman’–who won the Gold Medal in the 400m race at the 1924 Paris Olympics. Fast-forwarding 99 years to the present 2023…imagine that Eric Van Steerteghem runs a long distance from A to B at an average speed of 3 metres per second. On the way back from B to A (following exactly the same route as before, only in the opposite direction, and naturally more tired than before), Eric’s average speed is 2 metres per second.

The brainteaser is to figure out Eric’s average speed for his entire run from A to B to A. (Being an expert in Physics, Mathematics and more, Jens could tell you immediately that the average speed will not be 2.5 metres per second! Can you do like Jens and figure out the correct value?)


Thinking of delicious Chinese food…
rearrange the letters of PRC CALORIES
to make a proper 11-letter English word!


Part 1: As a very quick warm-up before the main Part 2, imagine a cube with its dimensions (equal length, width and height) in centimetres (cm).

If a particular cube’s volume (in cubic centimetres) is numerically equal to its total surface area (in square centimetres), then what must be the cube’s exact dimensions?

Part 2: If the length, width and height of a certain cuboid are all exact whole numbers of centimetres, and if the cuboid’s volume (in cubic centimetres) is numerically equal to its total surface area (in square centimetres), then what is the maximum possible height of the cuboid?

Multiplication Magic Square, Beautiful Billion Brainteaser! 😊β™₯😊

Your super-fun brainteaser challenge is to find nine different positive whole numbers
to fill the nine grid boxes (with one number per box) so that the
total product (when you multiply all the nine numbers together) will be 1000000000 = 1 billion.
Also, the mini-products of the three numbers in any row or in any column or in either of the two main diagonals should always give the same results in each of those eight cases.
That is: three row products, three column products & two main diagonal products
must all equal each other.


For this puzzle, we need to know that, in Mathematics, the reciprocal of any non-zero number n is 1 Γ· n.

Imagine that a lady on her birthday today said, “The difference between the reciprocal of my new age now and the reciprocal of the age I’ll be in a year from now is equal to the reciprocal of the year when my younger sister was born.”

Your brainteaser is to figure out the lady’s new age now, and figure out the exact year when the lady’s younger sister was born.

You know that I like the number 141, as it features in one of my email addresses, Here in blog post #146, I should give a special mention to the number 14641, which equals the fourth power of my house number 11 😊


Part 1: In our normal base ten, the number 146 = 6 x 1 + 4 x 10 + 1 x 10 squared.

However, in another base B (not base ten), 222 (base B) = 146 (base 10).

Figure out the value of B.

Part 2: This involves a new base, N. We are told that

222 (base N) = xyz (base 10),

where xyz represents a proper three-digit whole number.

The brainteaser is to figure out the maximum possible value of xyz, and the corresponding value of N.

A Wee Dose of Chess To Finish! 😊β™₯😊

Part 1: Though White is down on material, it’s White to play and win.
Part 2: If it were actually Black to play, what would be the strongest move?

It’s my intention to publish solutions to all the puzzles around the time that blog post #147 comes out, God-willing as always.

In the meantime, please do feel free to send me your best solutions to any or all of the puzzles, if you like 😊.

I would like to round off this article now by most sincerely wishing you a very blessed weekend, with lots of happiness in everything that you do β™₯

With kindest wishes as always,

Paul M😊twani β™₯

P.S. = Puzzle Solutions!


Eric’s average speed for the entire run was 2.4 metres per second. That can be verified using the formula Average Speed = 2vw Γ· (v+w), in which v=3 and w=2, the respective speeds for the outward and return runs covering equal distances.

PRC CALORIES can turn one’s diet upside down because they make RECIPROCALS !! 😊

Regarding length L, width W and height H, when a cube has L = W = H = 6cm, then its volume = 6 x 6 x 6 = 216 cubic centimetres, and the total surface area of its six faces is 216 square centimetres because each one of the faces has an area of 6 x 6 = 36 square centimetres.

In the cuboid part of the brainteaser, a maximum whole number height of 42cm is achievable when the length and width are 3cm and 7cm in either order.

Given that the volume was numerically equal to the total surface area, I used LWH = 2LW + 2LH + 2WH and then 1 = 2/H + 2/W + 2/L.

Letting L=3 helps to β€˜use up’ two thirds of the 1, leaving only one third or 2/6. So W can’t then be 6, but it can be 7, letting us solve directly for the optimal H.

(If the length and width are 4cm and 5cm in either order, we would find that H = 20cm; smaller than our optimal 42cm.)

In the Multiplication Magic Square, we must have the number 10 in the central box, and all the other factors of one hundred can be filled in the rows in (for example) this order (starting from the top-left box):- 20, 1, 50; 25, centre 10, 4; 2, 100, 5.

In the reciprocals brainteaser, the lady is 44 and her younger sister was born in the year 1980.

It makes use of the fact that 1/n – 1/(n+1) = 1/(n(n+1)). In the puzzle, n(n+1) has to be the year when the younger sister was born. The only value for n that gives a suitable value for n(n+1) in the reasonably recent past is n=44, and then n(n+1) = 44 x 45 = 1980.

In the number bases brainteaser, 222 (base N) has the value of 2 + 2 x N + 2 x N squared. If you were to generate an accurate table of different values for N and the corresponding values of 2 + 2 x N + 2 x N squared, it would show, for example, that 2 + 2 x N + 2 x N squared = 146 when N = 8 and 2 + 2 x N + 2 x N squared = 926 when N = 21 and 2 + 2 x N + 2 x N squared = 1014 when N = 22.

So, the answers asked for in the puzzle are:- B = 8; xyz = 926; N = 21.

In the Chess puzzle, 1 Bg5+ Kg8 2 Qh7+ Kf8 3 Qh8# is the fastest win for White.

If it were actually Black’s turn to move, then (though it’s true that 1…Qxg3+ would win easily) the quickest forced win is 1…Rh1+! 2 Kxh1 Qg1#, a key checkmating pattern 😊

Blog Post #137: VIPs Young and Old β™₯

Dear Readers,

Whether we have already met yet, or not, I think of you as a VIP because we are all children of God, and that automatically makes you a Very Important Person indeed.

Everyone who took part in a fun chess talk/’simul’ at Edinburgh Chess Club three days ago (in early celebration of the club’s 200th anniversary coming three days from now), received lovely prizes such as books, magazines and chocolates to let them all feel like the VIPs that they truly are β™₯

Thanks to Sue Loumgair, Dr. Vipin Zamvar, Ian Whittaker and FM Neil Berry (the President of Edinburgh Chess Club) for having sent nice photos from the event.

Dr. Vipin Zamvar is a really good-hearted gentleman who was particularly kind to my family during our final evening in Edinburgh β™₯

In addition to enjoying seeing very long-time friends Lindsay McGregor, David Montgomery, FM Craig Thomson, FM Neil Berry, Jonathan Grant, GM Keti Arakhamia-Grant & their daughter Elena Grant, it was lovely to get to make many new friends during the club’s joyful celebrations 😊😊

I would like to thank all who attended the chess talk for being a wonderfully receptive audience, and I congratulate everyone from the ‘simul’ for playing so many good moves. Special congratulations to Warrick Campbell and Neil Irving for taking full advantage of their opportunities and playing better than I did!

The title of ‘Funniest Chess Friend in Edinburgh’ probably has to go to Craig Thomson! He knows that 3 is my favourite number, but as I hadn’t seen him for 13 years (since 2009 !) and as his email address contains the number 17, I offer these amusing thoughts…I was obliged to score 17/19 in your honour, Craig…and also 1303 x 3 x 3 x 17 = 199359 in recognition of the fact that the club was precisely 199 years & 359 days old when we met three days ago! 😊😊

I promised Lindsay McGregor that I would publish the moves of a personal game that I also shared during the chess talk, as he was very interested in that game. Here it is:-

P.A.Motwani vs. My Computer (Training Game played at home on 27.8.2022)

1 e4 g6 2 d4 Bg7 3 Nc3 d6 4 Be3 Nf6 5 Qd2 0-0 6 Nf3 a6 7 Bh6 Bg4 8 h4 c5 9 h5 Bxh5 10 Bd3 Bxf3 11 gxf3 cxd4 12 Bxg7 Kxg7 13 Qh6+ Kg8 14 e5 dxe5 15 Ne4 Re8 16 Ng5 Qa5+ 17 Ke2 e4 18 fxe4 e5 19 Nxh7 Nxh7

20 Rag1 Qc7 21 Rxg6+ fxg6 22 Qxg6+ Kf8 23 Rxh7 Qxh7 24 Qxh7 Rd8 25 Bc4 Rd7 26 Qh8+ Ke7 27 Qxe5+ Kd8 28 Be6 Nc6 29 Qh8+ Kc7 30 Qxa8 Rd8 31 Qxd8+ Kxd8 32 Bd5 and White (then 2 pawns ahead) soon won… 1:0.

Here now is a selection of positions that occurred in the ‘simul’. In each case, it’s White to play and win.

At the moment, I can still recall the moves from the 19 games in the ‘simul’. After a while, I will probably forget some of the details, but I will always treasure having met all the lovely people at the club β™₯

Chess Position Solutions

  1. White obtained a decisive advantage via 1 Bxf6 gxf6 2 Qh6 f5 3 Qf6.
  2. White obtained a decisive material advantage via 1 Qd2 Ned7 (1…Ng6 2 f5 Ne5 3 h3 Bh5 4 g4 also traps Black’s queen’s bishop) 2 h3 Bh5 3 g4.
  3. White won with 1 Rxd7 Re4 (or 1…Qxd7 2 Qh6) 2 Rc7 intending 2…Rxh4 3 Rxc6 or 2…Qxc7 3 Qh6 or 2…Qd6 3 Qxe4.
  4. White won with 1 Nxd5, intending 1…exd5 2 Rxe8+ Qxe8 3 Bxf6 gxf6 4 Qxd5+.

After all that chess, let’s round off with a nice wee dose of Maths here in Blog Post #137…

Not only is 137 a prime number, but so is 13, 17 and 37. 137 is the smallest whole number with digits possessing such properties!

In honour of Edinburgh Chess Club’s 200th anniversary, 200 is the smallest whole number which cannot be made prime by changing one of its digits.

I would like to wish everyone a very happy All Saints Day now on 1 November β™₯

As there must surely be lots of singing in Heaven, the saying “Music is the Medicine of the Mind” comes happily to mind β™₯

With kindest wishes as always,

Paul M😊twani β™₯

Blog Post #130: British Senior (Over 50) Chess Champions and Unforgettable Friends β™₯☺β™₯

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.

Philip Crocker and me, joint winners of the British Senior (Over 50) Chess Championship (with Chris Duncan who had to leave a bit earlier). Afterwards, Philip and I had a happy interview with WIM Natasha Regan and GM Matthew Sadler, friends of mine from long ago. This British Championship was a very precious event, not only for getting to enjoy good chess, but also for seeing dear old friends again and making many new ones. I would like to thank all the organisers, arbiters, players and Chessable (the principal sponsor) for a most memorable event β™₯☺β™₯.
Continue reading “Blog Post #130: British Senior (Over 50) Chess Champions and Unforgettable Friends β™₯☺β™₯”

Blog Post #129: Happy Rainbows β™₯😊😊β™₯

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 β™₯😊😊β™₯

Jenny & Paul’s Wedding Day, 27 years ago β™₯😊😊β™₯

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.”

Photo of Paul taken by Jenny yesterday evening inside our favourite Kinepolis cinema!😊

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…

Paul with two great colleagues and a super student at Musica Mundi School 😊😊😊😊

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…

A magical moment captured beautifully in this photo by Erika Sziva β™₯😊β™₯

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!

60th birthday T-shirt to Paul from Nico β™₯😊β™₯

Erika and Robert now have two terrific chess sites. Their first one is

and, since February 2022, they’re also running

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.

Place an invisible white knight somewhere on the board so that it will
then be White to play and force checkmate in four moves β™₯😊😊β™₯

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 β™₯ 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

The forced checkmate in 4 moves is 1 Qe6+ Kf8 2 Nh5+ Ke8 3 Nf6+ Kd8 4 Qg8# β™₯

Blog Post #126: For Rooney, Claire, Sheila, Cansu, Jonathan, Erika, Robert, AndrΓ©e & other dear friends: may you all have very happy memories, birthdays or anniversaries this May β™₯😊β™₯

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.

For the Son of Man is going to come in his Father’s glory with his angels,
and then he will reward each person according to what they have done.
Matthew 16:27

Knowing the lovely tradition of dedicating the month of May to Our Lady, Mary, this is a perfect time to recall the following prayer:

Hail Mary full of Grace, the Lord is with thee.

Blessed are thou among women and blessed is the fruit of thy womb Jesus.

Holy Mary Mother of God,

pray for us sinners now and at the hour of our death

Our Lady Mary’s beautiful month of May β™₯
Continue reading “Blog Post #126: For Rooney, Claire, Sheila, Cansu, Jonathan, Erika, Robert, AndrΓ©e & other dear friends: may you all have very happy memories, birthdays or anniversaries this May β™₯😊β™₯”

Blog Post #83: Magical Duets!

Dear Readers,

My house number, 11, is a palindrome; so is 101 or 11 x 11 =121, but what about 11 x 101 x 11? The result 12221 is clearly palindromic, and it’s intended to let you know a very nice date for your diary: exactly three weeks from today, on 12.2.21, you’ll be able to enjoy on YouTube (at 19:30 Central European Time via and clicking on the banner there) a feast of fabulous, musical solo performances featuring many young talents of Musica Mundi School.

I have the pleasure of getting to teach Mathematics to every student who studies the subject at the school, and right now I have some delightful surprises starring Julija and Hoi Yuet.

Continue reading “Blog Post #83: Magical Duets!”

Blog Post #81: Top of the Class, Nice Niklas!!

Dear Readers,

It is with great pleasure that I thank everyone who participated in the ‘Good Lives Global Prize Competition’ (see Blog Post #80).

Andy H. from Scotland was the very first person to reply with all the mathematical puzzles completely correct. Andy loves challenge puzzles so much that he simply wanted to enjoy them without being given a prize. So, in recognition of his excellent attitude, we have a bonus puzzle in Andy’s honour, down below.

Before then, I want to congratulate Quintijn van Heek (an A-Level Maths student of mine) and Krissy Teng (another great student at the beautiful Musica Mundi School in Waterloo, Belgium) for also solving all the mathematical puzzles. Well done, Quintijn and Krissy!

Continue reading “Blog Post #81: Top of the Class, Nice Niklas!!”

Blog Post #72: Appreciation of Beauty

Dear Readers,

I love to see, and appreciate with an attitude of gratitude, so much beauty in the natural world God created, as well as in the kind faces, words and actions of people who reflect God’s love through the way they live.

A recent father and son photo.

Continue reading “Blog Post #72: Appreciation of Beauty”

Blog Post #70: Back to the 70’s!

Dear Readers,

Today, my family has been busily and happily congratulating my son’s lovely girlfriend on turning 22. My personal message included the following sneaky fun surprise…

  • Pick any three-digit whole number which has three different digits from 1 to 9 (e.g. 236)
  • Write down all the two-digit whole numbers that can be made from your chosen three-digit number without repeating digits in the same number (e.g. 23, 26, 32, 36, 62, 63)
  • Add up all your two-digit numbers (e.g. 23+26+32+36+62+63=242)
  • Divide your total by the total of the digits in your chosen three-digit number (e.g. 242/(2+3+6)=242/11=22 for the birthday celebration today!)

Continue reading “Blog Post #70: Back to the 70’s!”

Blog Post #48: Maths Enrichment and Fun from Cambridge

Dear Readers,

I am currently enjoying preparing a β€œMagic Maths” show packed with super-fun puzzles for my colleagues and students at Musica Mundi School, Waterloo. For inspirational sources of material, I use lots of good things from what is still beautiful in the world around us. Also, I reflect on all that I have read and learned from very fine books linked to the Cambridge Maths courses that my students are following. Continue reading “Blog Post #48: Maths Enrichment and Fun from Cambridge”