December 2021 – Paul Motwani

Blog Post #121: Sure Way Home ♥♥♥

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:-

A photo from 11 years 4 months & 4 days ago = 4144 days ago;
SUCH TIME ON EARTH IS LIKE A MOMENT OUT OF JOYFUL ETERNITY SURE TO COME ♥♥♥

BIBLE VERSE MATTHEW 1:21 ALWAYS GIVES GREAT COMFORT
(& it’s a reassuring reminder here in Blog Post #121),
SO WE CAN LIVE WITH FULLY JUSTIFIED HOPE, JOY & PEACE THROUGHOUT OUR LIVES

Another favourite photo is the following stunning view of the French Alps that people shared via Facebook recently.

What thoughts come to your mind when you see this magnificent picture?
Personally, I think of our journey on Earth leading to Heaven.
It need not be feared. With trust in God, every step can be enjoyed gratefully.
That’s the sure way home.

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.

Istanbul, the largest city in **TURKEY** 😊

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.

The three trees are similar yet different for now.

I am going to move just one single number from one tree to another tree.

Can you read my mind and tell me which number I’ll move to which tree, and why?

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 ♥.

PROVERBS 23:7–“As You Think, So You Are” ♥

I know lots of people who love a good chess puzzle, and so let’s enjoy the following…

White has an invisible pawn somewhere on the f-file.
Where exactly should it be placed so that it will then be
**Black** to move and force checkmate in just 3 moves?

I would like to conclude now by wishing everyone a very blessed, joyful Christmas and a happy new year coming soon, too.

The best teacher of all opened hearts with His perfect love ♥♥♥

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.

Blog Post #120: Prepare Your Heart ♥

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 😊.

A nice photo from my friends’ town of Kolbotn

Easy Mindreading Puzzle: Rearrange the letters of OWNS
to get the cool word that I’m thinking of…😊

In Norway, they of course have lots of SNOW even when it’s not Christmas!!

Could this old photo of Kolbotn be from the year A*(100-A) nearly 100 years ago?

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)…

Happy memories of enjoying Maths puzzles with Vilja, Ask-Johannes and Sigurd August in Waterloo, Belgium, several years ago 😊

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!

Congratulations for realising that, since V = Y1 + Y2, the value of V must be (100 – 4 – 74) ÷ 2 = 11 😊

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 😊

I think there might be at least four smiles that big in Norway tonight!
Merry Christmas, dear friends! ♥

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.

For Vilja, Ask-Johannes, Sigurd August and all keen chess fans:
It’s White to play and force checkmate in only 3 moves 😊😊😊

I wish everyone a very happy Christmas and New Year coming soon.

With love and kindest wishes,

Paul M😊twani xxx

There are many reasons for why 3 is my favourite number

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 ♥

Blog Post #119: Love Whispers So Our Hearts Can Sing

Dear Readers,

“Every heart sings a song incomplete, until another heart whispers back” are deeply moving words from Plato…but the perfect heart of God is whispering lovingly to us. When we take the time to turn down the busyness and distracting noise of the world, then we can hear God whispering tenderly to guide us gently along the paths that He knows will ultimately lead us safely and joyfully home, to Heaven. This Advent is the perfect time to pause well, to listen, to hear and respond to God’s personal call to each of us.

Let Our Hearts Sing Together With Thanks To God ♥ ♪ 😊 ♪ ♥

“Sing to the Lord with thanksgiving”–Psalm 147:7

“Sing and make music from your heart to the Lord”–Ephesians 5:19

“I fine-tuned my ear to the sayings of the wise, I solve life’s riddle with the help of a harp”–Psalm 49:4, The Message Bible.

I know that I am really blessed to be teaching Mathematics in the beautiful Musica Mundi School. So, here in Blog Post #119 exactly 19 days before Christmas, I offer a selection of fresh riddles for everyone’s enjoyment.

Rearrange the letters of WISE + HARP to make A + a proper 7-letter word.

A Modern Harp has 47 strings & 7 pedals and is shaped somewhat like a number 7 😊

Congratulations for discovering that WISE + HARP = A + WHISPER !

2. The prime number 7 equals 3 squared – 2

and the prime number 47 equals 7 squared – 2.

What is the smallest positive whole number that is 2 less than the square of an odd number but is NOT prime?

3. Think of the oldest type of woodwind instrument. Remove its first letter. You now have a different musical instrument! Which one is it?

Here in this blog post, it’s nice that 119 is the answer to the second puzzle, above. 11 squared – 2 = 121 – 2 =119. It might plausibly ‘look’ prime at first sight, but it’s actually a composite number since 119 = 7 x 17.

4. Q: How can you get the most beautiful music ever?

A: Compose it!

Q: Make a proper nine-letter word using all the letters of COMPOSE IT.

A: 119 is a clue; it’s COMPOSITE! 😊

5. Can I rely on you to think of a musical instrument that is an anagram of RELY !?

I would like to round off now by wishing everyone a very happy period of Advent leading to a joyful Christmas coming soon.

With kindest wishes as always,

Paul M😊twani xxx

Michael wrote down the total number of dots on all the faces of the dice *except for the bottom*. I wrote down the total number of dots on *just the top and bottom* faces. What is the correct result for Michael’s number *multiplied by* my number?

Congratulations for figuring out 17 x 7 = 119, a fun finish to Blog Post #119 😊

Blog Post #118: A Case Full of Fun for ‘Tiffany’😊

Dear Readers,

To cut a long story short, I needed a fun code name for a friend whose birthday is coming up fast, and I was thinking…if any fast…idea comes…when suddenly that was it! She can be named as ‘Tiffany’, partly because as Tiffany is an anagram of if any fast, and partly because Tiffany Case in the 1971 film ‘Diamonds Are Forever’ has remained, for half a century, one of my absolute favourite female characters ever in a 007 movie 😊.

Can you think of a classy English eight-letter word that can be made using all the letters of I TIFFANY ? Well, I’m pretty sure that ‘Tiffany’ (who’s really a very smart lady indeed) would find AFFINITY almost immediately.

I have an extra, special affinity for Blog Post #118 right here, because (unless I slow down a lot in future) it’s probably going to be the only one I’ll ever write where my age is half of the blog post number; in this case now, 59 = 118 ÷ 2.

Sending everyone warm wishes past the cold weather! 😊

An early Merry Christmas pic. from my classroom yesterday 😊!

Whenever in my life I might encounter the number 118 again…I will also think of Wout, an incredibly talented 12-year-old musician and super-gifted young mathematician at Musica Mundi School.

Pictured below, is part of Wout’s perfect solution to a fun wee prize puzzle that I sent on Wednesday night to everyone in the school, as we’re looking forward to celebrating several birthdays here this month.

18 is the only number in the left-hand column of the table for which an alternative solution (also using consecutive positive whole numbers) was possible: 5+6+7 makes 18, too.

How can we use Wout’s solution regarding 18 to find a sum of consecutive whole numbers that totals 118 instead of 18?

Well, 118 = 18 + 100 = 18 + (4 x 25), which prompts the idea of simply adding an extra 25 onto each of the four consecutive numbers that Wout used. In that way, 3+4+5+6=18 can be transformed to 28+29+30+31=118.

Time for another quick wee word puzzle/j😊ke…! I might ask my friend if any fit people come to her mind…to which she could respond with the practically perfect anagram, “People…I Tiffany“!

Enjoy your birthday, dear Tiffany, and I wish everyone a wonderful, happy weekend now t😊😊.

With kindest wishes as always,

Paul M😊twani xxx