Blog Post #122: A Lamp and a Light β™₯

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 😊.

Here’s wishing you a wonderful happy birthday, dear little sister xxx β™₯
White and Black each have one invisible minor piece,
of the same type, located somewhere on the d-file.
Then, it’s either Black to move and force checkmate in two moves,
or it’s White to move and force checkmate in three moves.
This delightful chess puzzle is from a real game that was played in 2012 😊.

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

Psalm 119:105–“Your Word is a lamp to guide my feet and a light for my path.”

Blog Post #121: Sure Way Home β™₯β™₯β™₯

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…

A very happy three 😊😊😊

…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 β™₯β™₯β™₯
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 😊😊😊

Thinking of Home in another dimension

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.
Β 
I am going to move just one single number from one tree to another tree.
Β 
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 β™₯.

PROVERBS 23:7–“As You Think, So You Are” β™₯

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 β™₯β™₯β™₯

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 β™₯

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.

God Loves All of Us

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
A lovely lake view at 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.

Have you got ’em?!

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) Γ· 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! β™₯

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
Have a Blessed Christmas

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 β™₯

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 β™₯ β™ͺ 😊 β™ͺ β™₯

“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.

  1. 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?

A photo from 47 years ago.

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

FLUTE – F = LUTE ! 😊

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 !?

The LYRE is a lovely instrument 😊

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 Γ· 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.

Wout’s Perfect Puzzle Solution 😊

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

Always Treasure Every Moment God Gives In Our Lives

Blog Post #117: Love Like A Child πŸ˜Š

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.

Dad with me at age 003 😊

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 an unforgettable class of 2012-2013 😊
A super-fun Magic Math Assembly with hundreds of happy children on 23.9.2015 😊
A charity chess fundraising event at St. Columba’s High School in Perth, Scotland,
in the early 1990s 😊
With Mum and her mother and my little brother in 1966 😊
With my dear little brother and my loving grandpa long ago, but never forgotten xxx

With love and kindest wishes as always,

Paul M😊twani xxx

Jesus said, β€œLet the children come to me. Don’t stop them! For the Kingdom of Heaven belongs to those who are like these children.”

Blog Post #116: 003 Birthday Fun for a Great Friend πŸ˜Š

Dear Readers,

Once in the theatre within my last school, I asked the audience jokingly, “Does anyone here, anyone at all, know Mr. Mo’s favourite number?” Something like 300 hands shot up instantly as every student knew that 3 had long been my absolute favourite number 😊😊😊.

A nice photo from l😊😊😊ng ago!

In my current school, the beautiful Musica Mundi School, I am agent 003 to some colleagues who bear bravely with my sense of humour!

Early this morning, I sent a double dose of birthday fun jokes and puzzles to a dear friend who turns 67 today, but of course it had to become a triple…and so here we are in ‘003 Birthday Fun for a Great Friend’!

Remove the digit 6 from 67.

Replace it with 93. My joke/reasoning is: “What’s the difference? 9-3 is still 6.” 😊!

Now my weary 937-year-old friend is invited to figure out 0.03 x 937.

In reality, it’s a piece of cake that should light up his eyes because the result of 28.11 is to wish him a most happy birthday today (28 November), and is definitely to wish all of you a lovely Sunday now, t😊😊.

HAPPY BIRTHDAY, ‘BIG BR😊THER’!

As my friend is a keen and good chess player, let’s round off with a freshly- baked homemade puzzle in which it’s either White to move and force checkmate in 003 moves OR Black to move and force checkmate in 007-003=004 moves!!

It’s either White to move and force checkmate in 003 moves
OR Black to move and force checkmate in 007-003=004 moves!! 😊

Congratulations, dear friends, for finding 1 Qd8+ Kh7 (or 1…Bf8 2 Qxf8+ Kh7 3 Bd3#) 2 Bd3+ Kh6 3 Qh4# for White or 1…Qb2+ 2 Kd3 Qd4+ 3 Kc2 Qc3+ 4 Kb1 Qb2#, checkmate for Black!

With kindest wishes as always,

Paul M😊twani xxx

P.S.

What happy message can you get if you start with the word EVOLUTION, remove a TON of letters, and rearrange the remaining ones?

My favourite true answer is: I LOVE U 😊

P.P.S.

In a joke that a friend posted a few days ago, a man tells his wife not to worry about her mistakes, but rather to embrace them. So, she immediately gives him a really big hug!

Blog Post #115: Happy Birthday Surprises for TimothΓ©e πŸ˜Š

Dear Readers,

This is the perfect day to post nice surprises for TimothΓ©e (a brilliant young pianist at Musica Mundi School) because it’s his birthday, he’s a keen chess fan, and today marks the start of the World Chess Championship between Norway’s Magnus Carlsen, the reigning champion, and his Russian challenger, Ian Nepomniachtchi. I can confirm that the first game (in progress right now) is already very exciting!

Where is the championship being held? I’ll answer that in the form of a wee puzzle/joke ! 😊

_ _ _ _ _ YOUR TICKETS TO _ _ _ _ _ !

The five ‘blanks’ at the end are for the name of the place, while the two + three ‘blanks’ at the start together sound practically the same as the place name, and we’ll get a proper six-word sentence!

Knowing where the Carlsen-Nepomniachtchi really is being held, my answer is: DO BUY YOUR TICKETS TO DUBAI ! 😊

Timothée and I always enjoy discussing a good game of chess 😊
Continue reading “Blog Post #115: Happy Birthday Surprises for TimothΓ©e πŸ˜Š”

Blog Post #114: For My Friend M.E. and for Mandy πŸ˜Š

Dear Readers,

What name can you think of involving just M and Y? This was a fun, quick, wee warm-up puzzle because M AND Y makes MANDY, in honour of a lovely friend of mine 😊.

Now get ready to solve for X !

Lots of Math problems say ‘Find X.’ Here, you can’t miss it!! 😊

Punny thoughts for a sunny day: Learn your trig. facts ‘n formulas at the beach!!
It’s all for a good cos., you’ll get a free tan…
and soon the teacher smiling at your work will be a bright sine! 😊
P.S. Congratulations for figuring out that the island is approximately 17.1 metres from the beach.
Continue reading “Blog Post #114: For My Friend M.E. and for Mandy πŸ˜Š”

Blog Post #113: Nice puzzles for 11.11 tomorrow

Dear Readers,

Alice, a young student who knows about the special significance of Armistice Day, 11.11, has the following conversation with Armand, her great-great-grandfather…

Remembering with Thanks

Alice: “Great-great-grandfather, my mum told me that you were born not very long after the end of World War I.”

Armand: “That’s right, Alice! As I know that you like Maths, I will tell you this: If you multiply my age now by my favourite whole number and then divide by the age I was last year, the final result should be 11.11.”

Alice: “Wow, that’s cool! I think I can figure out your age and your favourite number!!”

Armand: “Here’s a bonus puzzle: Make a proper 11-letter word using all the letters of CAN REMEMBER.”

Your fun challenge is to join Alice in cracking her great-great-grandfather’s puzzles!

Wander, ponder and wonder with Alice! 😊😊😊

I intend to publish solutions in a few days’ time.

With kindest wishes as always,

Paul Motwani 😊😊😊 xxx

P.S. Here are the puzzle solutions, being posted now on 12 November 2021:-

Armand is 101 years old and his favourite number is 11.

101 x 11 Γ· 100 = 11.11

CAN REMEMBER makes REMEMBRANCE.