Blog Post #139: Yo, Jens! πŸ˜ŠπŸ˜Š

Dear Readers,

This particular post is being written as a nice wee bonus surprise for Jens, a friend and brilliant colleague of mine at Musica Mundi School.

Jens solves lots of puzzles regularly, and he really – – – – – – them! The ‘blanks’ – – – – – – stand for a proper six-letter English word that can be made by rearranging the letters of the title ‘Yo, Jens! 😊😊’

The smiley faces 😊😊 also fit well with the answer, but as Jens especially enjoys mathematical puzzles, here comes a sneaky little one inspired by the name JENS. Regarding positions within the English alphabet, J=10, E=5, N=14 & S=19. As we’re now in blog post #139, your fun Maths challenge is to use the numbers 5, 10, 14 & 19 exactly once each in a calculation which leads to a result of 139. You may use the 5, 10, 14 & 19 in any order that you like, and you may also use +, -, x, Γ·, ( ) freely wherever you may wish to.

Via Blog Post #138, Jens discovered that my dad will turn 88 next month. I’m now thinking of two proper 2-digit numbers XY & YX such that the sum XY + YX = 88, while the product XY times YX is as small as possible (but neither X nor Y is zero). I’m also thinking of those particular numbers because XY times YX Γ· 100 gives the day & month numbers of Jens’ birthday in the form DD.MM. Now you can enjoy discovering when Jens’ next birthday will be! 😊

Jens also loves some good chess! In the position featured below (which I saw via Facebook earlier today), White is of course in a totally, easily winning position. However, what still makes for a delightful wee puzzle is: How can White (to move) force checkmate in only 2 moves…?

White is to move and force checkmate in only 2 moves β™₯

It’s my intention to wait at least a day or two before publishing solutions so that, in the meantime, readers can enjoy tussling with the puzzles. You are most welcome to send me any/all of your answers, if you like…and now I have a beautiful Bible reflection to conclude this article.

“Therefore, encourage one another and build one another up, just as you are doing”-1 Thessalonians 5:11

Here’s wishing everyone a very good and peaceful Sunday now,

Paul M😊twani β™₯

P.S. = Puzzle Solutions (being posted on 26.11.22)


5 x (10 + 14) + 19 = 139.

XY + YX = 17 + 71 = 88


XY times YX Γ· 100 = 17 x 71 Γ· 100 = 12.07 in honour of Jens’ birthday 0n 12 July.

In the chess puzzle, White can underpromote the c-pawn to a new bishop! So, instead of 1 c8=Q?? which would produce a stalemate position, White forces checkmate via 1 c8=B! Kxe8 2 Rg8# 😊

Blog Post #138: With One’s Whole Heart β™₯

Dear Readers,

A particularly beautiful Bible verse is “I give thanks to You, O Lord my God, with my whole heart, and I will glorify Your name forever”-Psalm 86:12. That verse is inspirational because it reminds us that we give glory to God by doing everything with gratitude to Him.

Earlier today, my son and I had a nice chat while I drove him to Brussels Zaventem Airport for a special weekend trip that he’s making. On my way back home afterwards, I spotted a vehicle with an interesting number plate which led me to making a fascinating investigation into properties of numbers. For me, it was like receiving a surprise gift. I’m going to share it with you now, and I wish you lots of enjoyment too β™₯😊😊β™₯

I like my house number, 11, but my absolute favourite number is 3. So, I invite you to write down a three-digit number 11N in which N is any digit that you like from 0 to 9. Now calculate N x 11N, and let’s call the result your Star Number.

Next, we’ll shake things around a wee bit 😊 because I’m going to ask you to calculate 1N x 10N (where 1N is a two-digit number and 10N represents the three-digit number with digits 1, 0 and N). That new result will be your Super Star Number.

Question 1.1: What is the relationship between your Super Star Number and your Star Number?

If N is now any whole number (which can even be as big as you like), then N x (110 + N) is clearly not prime because it’s a product of numbers N & (110 + N). Even 1 x (110 + 1) is not prime because 1 x 111 = 111 = 3 x 37, a composite product.

Question 1.2: Is 1000 + N x (110 + N) prime or not?

Part of the license plate number that I saw today was 819.

Question 1.3: Can you show why 819 is a possible Star Number?

Question 1.4: Can you show why 1819 is a possible Super Star Number?

Here in Blog Post #138, let’s note that 138 = 2 x 3 x 23.

Question 1.5: 1819 raised to the power of P results in a 23-digit whole number. What is the value of P? Also, can you calculate the exact 23-digit result!?

Question 1.6: (138 x P Γ· 3) raised to the power of (3 x 3) also results in a 23-digit whole number. Can you calculate that 23-digit result precisely, too!?

Question 1.P: Can you spot a special connection between the 23-digit results of questions 1.5 and 1.6 ?

It’s my intention to wait a day or two before publishing solutions so that, in the meantime, readers can enjoy tussling with the puzzles. You are most welcome to send me any/all of your answers, if you like…and now I have more goodies for you!

My dad is not a chess player, but I think that he’ll like the fact that I’m now going to feature a truly fantastic old chess study from Germany (in which it’s White to move and force checkmate in 5 moves) in early celebration of his birthday coming up soon, on 5 December β™₯😊β™₯

Question 1.8: By the way, how old will my dad be then (on 5 December) if I tell you that his new age + his age 38 years before then will equal 138 ?

Brilliant Old Chess Study from Germany (also shared recently by others on Facebook)

It’s White to move and force checkmate in 5 moves !

Early Christmas Word Puzzle β™₯😊β™₯

Remove a particular letter from GERMANY and then rearrange the remaining six letters to make a proper 6-letter English word which relates to Christmas. There is just one, unique solution.

I will finish now by wishing you and everyone a wonderful, happy weekend.

With kindest wishes as always,

Paul M😊twani β™₯

P.S. = Puzzle Solutions (being posted now on 13.11.22)

1.1 The Super Star Number is always exactly 1000 more than the Star Number.

1.2 Since 1000 + N x (110 + N) is actually the same as the product (10 + N) x (100 + N), it’s always composite; never prime.

1.3 819 = 7 x 117, and is therefore one possible Star Number (with N = 7).

1.4 1819 = 17 x 107, and is therefore one possible Super Star Number (also with N = 7).

1.5 P = 7, and 1819 raised to the power of 7 gives the 23-digit result 65891424018613967932339.

1.6 (138 x 7 Γ· 3) raised to the power of (3 x 3) gives the 23-digit result 37213699403613156884992.

1.7 It’s not so easy to spot at a glance that the two 23-digit results actually contain exactly the same 23 digits (in two different orders, of course) ! β™₯

1.8 88 + (88 – 38) = 138. My dad will be turning 88 on his birthday next month β™₯

Brilliant Old Chess Study Solution

The incredible, most powerful, centralising move for White from the chess study position given earlier is 1 Qe4!!, intending Qb1 followed by Qb5# or Qb6#.

Note that 1…Bxe4 would allow 2 Rc5#,
while after 1…Rxe4 (or 1…Qxe4) 2 Rh8, Black cannot prevent 3 Rc8# !

Black sees that 2 Qb1 is threatened, and 1…Nd2 loses to 2 Qe3, for example.

My favourite variation in this stunning study is probably 1…Qf3 (to answer 2 Qb1? with 2…Qb3!) 2 Qd4!! Rxd4 3 Rh8 Be4 4 Rc8+ Kd5 5 Rc5# β™₯😊β™₯

Another line is 1…Qg1 2 Qb1 Qc5 3 Qb4!! (even stronger than 3 Nxc5) 3…Qxb4 4 axb4 and 5 b5# cannot be stopped!

Early Christmas Word Puzzle Solution

GERMANY – Y gives GERMAN which rearranges nicely to make MANGER for Christmas coming soon β™₯

Special congratulations to my friend and brilliant colleague, Jens Van Steerteghem (one of the Science teachers at Musica Mundi School), who sent in terrific answers to many of the mathematical puzzles. Feel free to now enjoy Blog Post #139: Yo, Jens! 😊😊

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 #136: Chess Greetings To Friends Worldwide β™₯😊😊β™₯

Dear Readers,

Due to being busy working as the Mathematics teacher at the beautiful Musica Mundi School in Waterloo, Belgium, I don’t currently play many competitive chess games, but I do still very often think of dear chess friends all over the world. For instance, I would like to wish a super-happy birthday for tomorrow to Anuurai Sainbayar, a lovely lady chessplayer whom I met in August at the British Championships in Torquay with other friends there, including Gregg Hutchence, GM Keith Arkell and Midhun Unnikrishnan.

Happy memories from Gregg’s birthday on 14 August in Torquay β™₯😊😊β™₯

We all laughed a lot there, and now, here in Blog Post #136, I have a sort of mathematical curiosity/tongue-twister for everyone, featuring the number 136 ! It’s this: 136 is the sum of the cubes of the digits of the sum of the cubes of its digits !! Let’s see why that is so… First, 1 cubed + 3 cubed + 6 cubed = 1 + 27 + 216 = 244. Then, 2 cubed + 4 cubed + 4 cubed = 8 + 64 + 64 = 136 β™₯😊β™₯

Early Birthday Puzzle about Anuurai β™₯

As it’s 18 October today, I offer you this quick, fun puzzle about the new age that Anuurai will be on her birthday tomorrow… The sum of the squares of the digits in Anuurai’s new age will be 18. What will be Anuurai’s new age? Feel free to send in your answer, if you like β™₯😊β™₯

Tuesday lunchtimes are special treats this year at Musica Mundi School because we have a fun club for all students, teachers and other friends here who are interested in playing and discussing fascinating chess games and puzzles.

RaphaΓ«l is one of the very bright and talented, young mathematicians
who also loves chess at the school β™₯

As I know that Emile, Guillaume, Hoi Yuet, Jan V-L, Peter The Great, Raphaël, Steven, Timothée, Wout and others love sparkling attacking chess moves just as much as Anuurai does, we had several wonderful examples today 😊

It’s White to play & win
It’s White to play & win by force in this elegant study by A.Troitsky
It’s Black to play & win quickly
It’s White to play & win in this early birthday chess treat for Anuurai
(which is actually a study from almost 136 years ago!!) β™₯

Have a wonderful day, dear friends, and keep a smile on your face and a rainbow in your heart β™₯😊β™₯

With kindest wishes as always,

Paul M😊twani β™₯

P.S. = Puzzle Solutions

  1. White wins with 1 Bxh6!, intending 1…gxh6 2 Qg6+ Kh8 3 Qxh6+ Kg8 4 Rae1 Qd6 5 Qg5+ Kh7 6 Re4 Qg6 7 Rh4+ and the loose bishop on c5 will be captured for free.
  2. The line 1 Qd2+ Kc5 2 Qb4+ Kd5 3 Qc4+ Kd6 (or 3…Ke5 4 Qc5+ Ke4 5 Qc2+, skewering Black’s king & queen) 4 Qd4+ Kmoves 5 Qa7+ emphasises the winning theme of skewers in this elegant study.
  3. Black wins quickly with 1…exf2++ 2 Kxf2 (or 2 Kd2 Qe1+ 3 Kc2 fxg1=Q) 2…Qe1+ 3 Kf3 Qg3#.
  4. White avoids promoting the h-pawn to a queen or bishop (which would result immediately in stalemate), and instead wins with 1 h8=R Nb1 2 Rh1! c3 3 Rh4! Na3+ (3…Nd2 is similar) 4 Kxc3 Nb1+ 5 Kc2 Na3+ 6 Kb3 Nb1 7 Rd4 (7 Rh2 is equally effective) 7…Na3 8 Rd2 and mate follows on White’s next move! β™₯

May the God of hope fill you with allΒ joy and peace in believing, so that by the power of the Holy Spirit you may abound in hope.” Romans 15:13

Blog Post #135: A Gift from God β™₯

Dear Readers,

“Children are a gift from the Lord; they are a reward from Him” is Psalm 127:3, a particularly beautiful verse from The Bible. Today, my wife, Jenny, and I thoroughly enjoyed a wee trip to the lovely city of Mechelen with our son, Michael, in advance of his birthday tomorrow.

Tomorrow, Michael’s age will be the smallest positive whole number which has precisely eight divisors (or factors) including 1 and the number itself. Your first fun challenge is to figure out the new age that Michael will be tomorrow…

The name Michael is actually of Hebrew origin, and one meaning of Michael is gift from God.

If you look back to Blog Post #134, there were many joyful surprises for Leonid Kerbel (and his wife, Hagit, the founders of Musica Mundi School where I work as the school’s Mathematics teacher), as Leonid was turning 60. Their adult son, Liav (whose name is also of Hebrew origin and means God is Mine), will have his birthday on a day number this month which matches Michael’s new age for tomorrow. So, congratulations if you figured out already that Michael will be 24, and then you also know that Liav’s birthday is on October 24.

On his birthday, Liav’s new age will be a divisor (or factor) of this blog post number; that is, his age will be a factor of 135. Given that Liav is an adult and that his father, Leonid, is 60, there is only one proper possibility for the age that Liav will be…can you figure it out, fast!?

Well done for getting 27 = 135 Γ· 5; Liav will turn 27 on October 24.

Jenny and I already have some lovely surprises prepared for Michael tomorrow, and so now I’m going to offer an early, extra surprise for Liav, too! 😊

As Michael and Liav are both in their twenties, start with any number that is at least 20. It can be as big as you like, and it doesn’t necessarily even have to be a whole number. As it could be really large indeed (it’s your choice!) and it’s a surprise for Liav, let’s call your chosen number L. A calculator will come in handy regarding the following steps!

Calculate 1 Γ· L, which is going to give you a small decimal.

Let’s add on 1 as an early birthday bonus for Liav.

Using the number that you now have, raise it to the power of L.

Multiply by 10, the total number of letters in Liav Kerbel.

Round your result to the nearest whole number.

I have my fingers crossed that you’ve ended up with 27, as an early celebration for Liav! 😊

Just like Mathematics, the Royal Game of Chess is full of almost endless delightful surprises, and I’ve got an absolute beauty (based on a celebrated chess study) to share with you now β™₯😊β™₯

It’s White to move and force checkmate in 5 moves.
If you’re a chess enthusiast, I think you’re going to love this puzzle! β™₯😊β™₯

I would like to round off this article by wishing everyone a wonderful weekend. God bless you all.

With kindest wishes as always,

Paul M😊twani β™₯

P.S. = Puzzle Solutions

In the chess puzzle, White forces checkmate with 1 Nf6+!! gxf6 2 g6!! fxg6+ 3 Kxf6 g5 4 Kf5 g4 5 hxg4# ! β™₯😊β™₯

It’s worth noting that Black had no ways of trying to deviate and escape from the above sequence; all of Black’s moves were forced, completely!

“Every good and perfect gift is from above, coming down from The Father” James 1:17

Blog Post #134: Lovely Surprises for Leonid β™₯😊😊β™₯

Dear Readers,

Today at Musica Mundi School in Waterloo, Belgium, there were wonderful, joyful celebrations in honour of one of the school’s co-founders, Leonid Kerbel, a world-class violinist who will turn 60 in a couple of days’ time on Sunday, 9 October.

Lots of beautiful, musical treats and personal messages from many of Leonid’s family members, colleagues, students and other friends made for an unforgettable birthday celebration, which included a delicious lunch in the school β™₯

As I am employed by Leonid and his wife, Hagit Hassid-Kerbel, as the school’s Mathematics teacher, I have enjoyed preparing some extra, fun surprises 😊

Start by writing down any proper three-digit whole number that you like (such as 134, for example).

Repeat your number to now get a six-digit number (e.g. 134134).

Divide by 7, the total number of letters in VIOLINS.

Next, divide by 11, the total number of letters in COMPOSITION.

Now divide by the three-digit number that you started with…

Your result should be Leonid’s personal favourite number, 13 😊

It’s also very fitting that 13 is the total number of letters in HAPPY BIRTHDAY β™₯

Have a super-happy 60th birthday, dear Leonid.
Here in Blog Post #134, the number 134 is calling out to say,
“(1+3) x (1+4) x three is nice to you from me!” β™₯😊β™₯
Hagit & Leonid’s blossoming school brings beautiful music to many ears β™₯

What type of lovely little bird that loves to sing is hidden among the letters of LEONID KERBEL?

The one I’m thinking of is a ROBIN, also because the average length in centimetres of an adult European Robin is about 13, Leonid’s favourite number !

Beautiful photo of a robin by WGM Erika Sziva, a Woman Chess Grandmaster, who runs the sites & together with her husband, Robert Klomp.
You can enjoy a short, delightful video of a robin singing via this link:
Let’s have some more surprises now for Leonid! 😊

Write down any two numbers which add up to Leonid’s favourite 13 (e.g. 6 & 7 or -1 & 14 or 1.5 & 11.5, for example).

Multiply your two numbers together, and we’ll call the result your Star Product *

Now look back to your two starting numbers (which added up to 13). Add on my favourite 3 to each of them (e.g. 6 & 7 or -1 & 14 or 1.5 & 11.5 will then become new numbers 9 & 10 or 2 & 17 or 4.5 & 14.5, for example).

Multiply your two new numbers together, and we’ll call the new result your Super Star Product **

From your Super Star Product **, subtract your earlier Star Product *

Now add on 52, the number of whole weeks in a year…

I’m hoping that your final result was a happy hundred, to wish Leonid & Hagit 100% joy throughout the whole year, and far beyond! β™₯😊😊β™₯

Their first reactions to the unusual musical notes around the page border coming next might include shock, surprise, laughter,…,but they’re there for a happy reason, as you’ll discover in a few moments…

In this Magic Square, the sum of the numbers in
each of the rows, columns or main diagonals is exactly 60 for Leonid 😊.
The middle row is nice because, with just a wee extra touch of imagination,
we can see there 2018 and 2022 in honour of the year
when Musica Mundi School opened, and the current year that we’re still enjoying now β™₯
The musical notes in the page border may seem to be the wrong way up,
but if we look again…they’re all like hands clapping and giving Leonid a standing ovation
for his daily jokes!! 😊
If you like this 007 film reel tin and James Bond movies, then you may also like the fact that
REEL LIKE BOND rearranges perfectly to give LEONID KERBEL !! 😊😊
I’ve prepared a super-sneaky, brand-new type of Chinese takeaway from Belgium for Leonid…

Start with BELGIUM

Take away the Chinese name LIU

We now have BEGM

The positions of those letters within the English alphabet correspond to the numbers 2, 5, 7 and Leonid’s favourite 13 (for B, E, G & M, respectively)

Multiply together 2 x 5 x 7 x 13 and we get 910, nice for Leonid’s 9 October or 9/10 birthday! β™₯😊β™₯

I am just a few months older than Leonid, but we were both born in the year 1962. Now I have a special brainteaser to offer about Leonid & myself, but I reckon that a very good number of my colleagues and students and other readers could well succeed in solving it. I’m always really pleased when people like to try the puzzles and send me in their best solutions. 😊

This puzzle is set many years into the future, but the thought is offered very happily with hope and faith. What age will Leonid be if I can say to him with both of us live at that future time, “The product of my age 13 years ago and my age 13 years from now, divided by your age now is equal to your age now”? (Note: the words “…your age now…” refer to Leonid’s age then, at the moment when I’m speaking to him.)

A remarkable detail about that brainteaser is that there’s actually only one unique, same solution no matter who’s speaking! In other words, I didn’t need to mention any birth year or specific people or relative ages of the people involved. That would certainly have made the brainteaser tougher, but the unique solution would not change at all!

Leonid & Hagit are happy that I run a Chess club in their school. So, let’s almost conclude this article with a neat chess puzzle β™₯😊😊β™₯

The fun puzzle is to first discover exactly where Black has a new, invisible bishop somewhere on the c-file such that it will then be Black to play and force checkmate in 3 moves β™₯😊β™₯
I intend to publish solutions on Sunday, when Leonid turns 60 β™₯

In the meantime, I wish everyone lots of love, blessings and a very happy weekend β™₯😊β™₯

With kindest wishes as always,

Paul M😊twani β™₯

“Every good gift and every perfect gift is from above, coming down from the Father” James 1:17

Faithful friends are gifts from Heaven β™₯

Joke: What would Winnie the Pooh get by crossing Piglet with a violin?


P.S. = Puzzle Solutions

In the birthday brainteaser, congratulations to Jens Van Steerteghem for finding the unique solution. The future conversation referred to in the puzzle would have to be occurring sometime between 13 June and 8 October in the year 2047, when I would be 85 years old, but Leonid would be 84; not turning 85 until 9 October 2047. (85 – 13) x (85 + 13) Γ· 84 = 84. That’s the only solution with positive whole numbers to the equation (y – 13)(y + 13) Γ· x = x.

In the chess puzzle, with Black’s invisible bishop on c4, 1…Be3+! 2 Kc3 (2 Kxe3 or 2 Kd1 allow 2…Qe2#, while 2 Kc2 Qd3+ 3 Kb2 Qb3# is also a neat checkmate!) runs into 2…Qd3+ 3 Kb2 (or 3 Kb4) 3…Qb3#.

Blog Post #133: More Muffins for Michail!, Part II β™₯😊😊β™₯

Dear Readers,

Every day that I work as the Mathematics teacher at the beautiful Musica Mundi School in Waterloo, Belgium, I am truly grateful for everyone and everything there…including the very yummy muffins, of course!!

Even when the muffins have been gobbled up by lots of appreciative teachers and students, we continue to be blessed with really good meals and extra treats, too β™₯

A super-fun puzzle to go with this lovely photo is this:
start with SCHOOL EAT, and add just one more well-chosen letter.
Then rearrange the 10 letters that you’ll have to make a proper 10-letter English word.

There are only two possible solutions, and it’s quite beautiful that both solutions are in the photo! Can you discover both of the correct solutions? 😊😊

Looking back to Blog Post #132, which is now complete with full solutions to the puzzles given there, it turned out that

17 bananas would balance 21 muffins, in the context of the picture below.

However, imagine checking it very late at night when you’re probably really tired,
and just making a small slip of putting 21 bananas & 17 muffins instead of 17 bananas & 21 muffins…

Naturally, the 21 bananas will be too heavy, but still, by considering this situation, we can enjoy the following very worthwhile bonus puzzle…

It’s this: How much heavier, in total, is 21 bananas & 17 muffins than 17 bananas & 21 muffins?

I really like that puzzle, because again it’s possible to solve it without even needing to know the individual masses of either a banana or of a muffin!

In the case with the 21 bananas & 17 muffins, we basically have 4 extra bananas but 4 fewer muffins when compared with 17 bananas & 21 muffins.

If we ‘lose’ a muffin but ‘gain’ a banana, we basically gain 20g, because a banana is clearly 20g heavier than a muffin, in the right-hand part of the diagram above.

Therefore, if we ‘lose’ 4 muffins but ‘gain’ 4 bananas,

we gain 4 x 20g = an overall gain of 80g. That’s it! 😊

Congratulations if you discovered either or both of these word puzzle solutions:




Over the coming days, many of my colleagues, students and other friends have their birthdays. In one case, the daughter of a colleague of mine will be turning 003 x 007 = a ‘lucky’ 21 years old 😊.

Today, it occurred to me that the last time I actually saw Raymond Dolan (a great chess friend and Facebook friend of mine) was more than 21 years ago! However, I so loved a photo and reflection about autumn that Ray posted on his Facebook page today, that I’m now re-sharing it with y😊u here β™₯

Thanks to Ray Dolan for having shared this lovely reflection via his Facebook page earlier today β™₯

Wishing everyone lots of love and blessings,

Paul M😊twani β™₯

“Let us not become weary in doing good, for at the proper time we will reap a harvest if we do not give up.” Galatians 6:9 β™₯

Joke: What kind of muffins can fly?

Plain ones!!

Blog Post #132: More Muffins for Michail!, Part I β™₯😊😊β™₯

Dear Readers,

Given that my wife, Jenny, and my son, Michael, and I all love good films, I offer you the following fun puzzle…

Nice photo taken by Jenny last Friday β™₯😊😊β™₯

Remove just one particular letter from FUN FILMS and then rearrange the remaining 7 letters to make a proper 7-letter English word. There is only one, unique solution, but I’m confident that you’re going to find it!

This past Monday, during lunchtime at Musica Mundi School, Michail (a Bulgarian student) and I laughed as he put a chunky chocolate muffin on his tray when I told him that I had solved a Maths puzzle involving muffins earlier that very same day!

On the left, the very nice Noetic Learning picture shows that
a 190-gram mass is balanced by one muffin & one banana,
while on the right we see that one banana is balanced by one muffin & a 20-gram mass.

My brand-new, fun puzzle for you (still based on the data in the above picture, though) is this: Imagine emptying the left and right pans of a balance scale, and then putting only bananas in the left pan, and only muffins in the right pan. How many bananas and how many muffins should be used so that the scale will be perfectly balanced? (Assume that the pans are large enough to accommodate all the goodies that are needed to do the job!!)

It’s possible to figure out the smallest number of bananas and muffins that will be required without even calculating their actual masses!

I’m always really pleased when students, colleagues, and other readers enjoy the puzzles and happily send me their best solutions, so please do feel free!

I hope you figure out the muffins like Michail…otherwise you might go bananas!!!😊😊😊

It’s my intention to give answers in a Part II sequel to this post β™₯

but before I sign off today, I would like to share a neat chess puzzle with you…

The puzzle is to locate White’s invisible knight somewhere on the f-file
and show how White can then force checkmate in 3 moves,
but not in 2 moves, due to the knight’s precise location.
My family and I wish everyone lots of love and, as a further wee bonus puzzle,
can you deduce whether the photo here was taken just before the one up at the top of this article, or just after that one!? β™₯😊😊β™₯

With kindest wishes as always,

Paul M😊twani β™₯

Corinthians 16:14 “Do everything in love.”


As another extra bonus, replace the letters FF in MUFFINS with CIA, and then rearrange the resulting 8 letters to make a proper 8-letter English word.

Magical Musician β™₯

Puzzle Solutions (being posted now on 29 September 2022)

If we remove the letter L from FUN FILMS, the remaining letters can be rearranged to make MUFFINS 😊

Imagine doubling up the left-hand scale to see that
*380g would be balanced by 2 muffins + 2 bananas.*

Now multiply the contents of the right-hand scale by 19 to see that

19 bananas would balance 380g + 19 muffins.

Next, use the ** result above to deduce that

19 bananas would balance 2 muffins + 2 bananas + 19 muffins

or 19 bananas would balance 2 bananas + 21 muffins.

Finally, subtract two bananas from each side

(which thereby still maintains balance) to get that

17 bananas would balance 21 muffins, and we didn’t even need to know the individual masses of either a banana or a muffin!

In the chess puzzle, it’s true that a white knight on f5 would enable 1 Rxg7+ Kf8 2 Rh8#, but that’s too quick in this puzzle!!

Instead, put a white knight on f7, and then we get to finish beautifully with 1 Rh8+!! Bxh8 2 Nh6+ Kf8 3 Rf7#, a lovely checkmate! β™₯😊β™₯

In the sneaky photos puzzle, we see that the gentleman wearing the red sweater has reached the shop by the end, and so that photo was taken moments after the earlier one. (He didn’t do something else just to trick all of us!!! 😊)

MUFFINS – FF + CIA leads to MUSICIAN β™₯

Blog Post #131: A Beautiful Double Discovery β™₯😊😊β™₯

Dear Readers,

The beautiful Musica Mundi School in Waterloo, Belgium (where I work as the Mathematics teacher) has been blessed now with many lovely new students and staff members as the school begins its fifth year, so far. As every person in the whole school family tries to give the very best of himself/herself, we can all learn so many good things from each other. With that thought in mind, I believe that, in a special sense, every person at Musica Mundi School can say honestly, “I teach at MMS!” (with regard to himself/herself personally). What makes that all the more beautiful for me is that it can be rearranged to make “Mathematics!”

I made that delightful discovery just earlier this year, around the time when I turned 60 in June. Only yesterday, though, God gave me a fresh gift which is similar in a way to the “Mathematics!” one, but is even much more important…

Continue reading “Blog Post #131: A Beautiful Double Discovery β™₯😊😊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™₯”