Month: December 2022

Blog Post #144: A Taste of Heaven ♥

Dear Readers,

We can see a piece of Heaven in places of peace on Earth ♥

When this day (19 December 2022) began, there were exactly six days = 144 hours until the start of Christmas Day ♥

By midday at the centre or heart of each new day, God has granted us another 144 super-precious 5-minute gifts of time (as 144 x 5→720 minutes = 12 hours), and it’s good to aim to use all of them to thank and honour Him in everything that we do ♥

I found today that ABCDF contains more than one interesting idea. Thinking of the product of the numbers that correspond to the normal positions of the letters, 1 x 2 x 3 x 4 x 6 = 144, right here in Blog Post #144. I count myself and everybody as being the missing ‘E’ for ‘EVERYONE’… I know that we will all go on to G, H, I, J, K, L…with God in Heaven provided that we believe gratefully In Jesus, King of Love ♥

We could note very briefly in passing that L→12, the (square) root of 144, but it’s really much more important to recognise properly that God’s Love for all of us is at the root of our salvation.

“For God so loved the world that He gave His one and only Son, that whoever believes in Him shall not perish but have eternal life”–John 3:16

As many of my students–and my colleagues–like puzzles, I’ll offer several now for everyone’s enjoyment 😊

Word Puzzles

Rearrange the letters of NEAR GIANT to make the name of a 9-letter country.

Rearrange the letters of MR TALENTS IN U to make a proper 11-letter word that all the students of Musica Mundi School use 😊♥😊

Numbers Puzzle

Use all of Cleo’s numbers 1, 6, 3, 6 and any operations that you want from +, -, x, ÷
to get the target number of 144. You may also use parentheses ( ) as you wish.

Special Puzzle in honour of my colleague Jens Van Steerteghem

JENS is a brilliant physicist, chemist & mathematician, too. Suppose that J=10, E=5, N=14 & S=19. Now here comes a super-fun puzzle…Add up the values of any two or any three of the four letters, then multiply by the left-over total, and divide by 4 in honour of JENS.

What is the maximum possible final result?

It’s a delightful wee Christmas present to Jens and everyone who loves mathematical puzzles, and in fact it’s possible to figure out the answer mentally using nice logic 😊♥😊

Puzzle Regarding A Lovely Lady (use A=1, B=2,…,Z=26 in this puzzle)

A former colleague of mine from my previous school in Belgium sent me a lovely Christmas card by email. In the lady’s six-letter first name, there’s no A. The product of the values of a certain four of the letters is 100. The product of the values of a certain five of the letters equals 5 x 144.

What is the exact product of all six letters? 😊

B😊NUS: Can you make a smart conjecture to guess the lady’s well-known first name, that many ladies have had?

A Really Beautiful Brainteaser ♥😊♥ (use A=1, B=2,…,Z=26 in this brainteaser)

Raphaël writes a proper six-letter English word that uses 5 distinct letters, including an R. The product of the values of all the letters in the word uses 4 distinct digits and begins with 5703…

Your mega-fun brainteaser is to figure out Raphaël’s six-letter word 😊

A Memorable Chess Game between Timothée and Raphaël at Musica Mundi School ♥😊♥

Chess Game in honour of my colleague Emile Daems

Emile Daems–a great colleague of mine at Musica Mundi School in Waterloo, Belgium–has been enjoying discussing some famous Chess openings with me. So, I’m including a photo of a recent game for Emile and other fans of The Royal Game ♥

Black’s sixth move, 6…Nd7!?, is rarer than 6…Ne4, but it’s very interesting 😊

A Whisky Puzzle in honour of my friends ‘Happy’ & Mandi!! 😊😊

Many people from Scotland and elsewhere enjoy some whisky! The word ‘whisky’ also brings ‘malt’ to mind, or the adjective ‘malty’. Here’s one description that I came across: “Generally speaking, a malt taste can be described as having a combination of flavours. It tastes sweet and nutty, but is also described as tasting similar to toast, caramel, coffee or fruits like raisins. The reason for its sweet, almost dessert-like taste has to do with how malt is made from barley.”

Here’s the puzzle now: Use all the letters of MALTY + H to make the name of a six-letter town where my friends ‘Happy’ & Mandi live, in the English county of Lancashire 😊

Here’s thinking of you, dear ‘Happy’ & Mandi 😊😊

A Maths Mega-Brainteaser is coming next, in honour of my students and my brilliant colleague Jens & his ingenious brother Nick Van Steerteghem (who wrote a computer program specifically to solve another recent brainteaser!–special congratulations also to Raphaël Murphy who solved the brainteaser directly himself!!)

Part 1

Imagine that I put the numbers 1, 2, 3, 4, 5, 6 & 7 (one of each) in a bag.

Raphaël, Tarik and Wout each take a number out of the bag.

Damla, Sophie and Jens also each take a number out of the bag.

I then announce, “The total sum of Raphaël’s, Tarik’s and Wout’s numbers is exactly equal to the total sum of Damla’s, Sophie’s and Jens’ numbers! Furthermore, the total sum of the squares of Raphaël’s, Tarik’s and Wout’s numbers is exactly equal to the total sum of the squares of Damla’s, Sophie’s and Jens’ numbers!!”

Your fun brainteaser is to figure out exactly which number is still in the bag.

Part 2 (Super-Tricky!!)

A large group of Maths fans goes with me to visit an old Spiritual Maths monk at a monastery on a high hill. The number on the monastery building is a proper three-digit number. When we get to the door and see the number, I tell everyone that the sum of the squares of its digits equals the monk’s age!

The monk’s age is also equal to the sum of the fourth powers of three distinct positive whole numbers (just meaning different from each other).

Your mega-challenge brainteaser is in three parts:-

2.1: How old is the monk?

2.2: What is the smallest possible three-digit number that could be on the monastery building, given the clues above?

2.3: What are the fourteen different possible three-digit numbers that could be on the monastery building, consistent with the clues? (Note: That’s fourteen answers including the answer to part 2.2.)

Note also that the Spiritual Maths monk is not hundreds of years old like Yoda!! The monk is at an age that many other people have reached, too, in human history. Of course, I didn’t strictly need to mention that. Even if the monk’s current age could have been, say, 144–or 22 years more than the oldest person on record to-date 😊!!–the first clue relating his age to the sum of the squares of the digits on the three-digit door number meant that he couldn’t be more than 9 squared + 9 squared + 9 squared, or 243 years old now!! Still, my sincere answer to the question, “What could be better than living to be 144+99 years old?” is: “Living forever in Heaven.”

It is my intention to publish full solutions (God-willing, as always) to Blog Posts #142 & 144 before 9 January 2023, when the next semester’s lessons at Musica Mundi School begin.

In the meantime, dear students, colleagues and other readers, please do feel free to send in your best solutions to any or all of the puzzles, if you like ♥

The school’s cats visit the Maths classroom frequently, and they’re already pondering the fresh puzzles now!! 😊😊😊

My family and I would like to wish you and everyone a very blessed, merry Christmas soon, followed by a wonderful, happy New Year ♥♥♥

With kindest wishes as always,

Paul M😊twani ♥

My colleague Solomon is embarking on a special journey very soon.
May God bless you in all that you do, dear friend ♥

Meanwhile, here’s wishing Headmaster Herman a very happy birthday tomorrow!

Enjoy a lovely piece in perfect peace! ♥

Certainly let any nice school cat add the missing ‘E’ (from much earlier in the article), because SCHOOL CAT + E = CHOCOLATES

for everyone…

…and add comes from 144 😊

P.S. = Puzzle Solutions (being posted on 31.12.2022)

NEAR GIANT = ARGENTINA

MR TALENTS IN U = INSTRUMENTAL

Using the numbers on Cleo’s sweater, (6×6)(1+3) = 36 x 4 = 144

In the puzzle about JENS, since J=10, E=5, N=14 & S=19 have a total sum of 48, we can achieve the optimal result with (10+14)(5+19)÷4 = 24 x 24÷4 = 144 again! 😊😊

In the puzzle about the lady’s six-letter name, the product of all her letter values = 3600, the LCM of 720 (= 5 x 144) & 100

Her name is DEBBIE (with 4 x 5 x 2 x 2 x 9 x 5 = 3600) 😊

Raphaël’s six-letter word is MEMORY, for which the product of the letter values is 13 x 5 x 13 x 15 x 18 x 25 = 5703750

(There were some cases to check, but since we were given that the word included an R–with letter value 18–the overall product had to be an even number and also a multiple of 9, and so in this particular puzzle the last digit had to be 0 & the sum of all the digits had to be a multiple of 9, which helped enormously to narrow down the cases for checking 😊)

MALTY + H = LYTHAM, where ‘Happy’ & Mandi live 😊😊

In part 1 of the Maths Mega-Brainteaser, 2+3+7=1+5+6 and, crucially, 2 squared + 3 squared + 7 squared = 1 squared + 5 squared + 6 squared; the unused number 4 is left in the bag 😊

In part 2, we don’t have to consider 4 to the power of 4 because that’s 256, which is a bit too old!! Instead, 1 to the power of 4 + 2 to the power of 4 + 3 to the power of 4 = 1 + 16 + 81 = 98, the monk’s true age ♥

Now we know that 98 = the sum of the squares of the digits of the monastery’s three-digit door number, which could be any of:-

149, 194, 358, 385, 419, 491, 538, 583, 707, 770, 835, 853, 914, 941

since 1 squared + 4 squared + 9 squared = 3 squared + 5 squared + 8 squared = 7 squared + 0 squared + 7 squared = 98 in those cases or permutations of them; clearly 149 would be the smallest possible proper three-digit door number meeting the monk’s requirements! 😊

Blog Post #143: Infinitely Precious ♥

Dear Colleagues, Students, Friends and All Readers,

Whether we already know each other, or not, my wish this Christmas for every human being is that each person will know that he/she is infinitely precious to God, our Creator.

Even if some of you might be younger than me, God thought of you (and me) long before I was born, way back on 13 June 1962. For simplicity here, if I were to count that official date on my birth certificate as my day #1, then today, 16 December 2022, is my day #22102. It’s a nice day on which to reflect back on 2022 and make sure that God is #1 at the centre–at the heart of my life–today and always.

Going along the cobbled Rue de la Croix that leads to the stunningly beautiful Musica Mundi School (MMS, where I am privileged to work as the Mathematics teacher with lovely students and colleagues) in Waterloo, Belgium, I paused yesterday morning to take some photos, because the breathtaking views of the land, the school, and the sky had God’s perfect stamp everywhere. Of course some things are man-made using gifts and talents that we have been given, but it’s good to recognise the true Creator.

Breathtaking views near Musica Mundi School ♥

Now, what about all the lovely people of the school community…? We currently have 40 students and around 43 staff members (including instrumental, theoretical, conducting and choir Music teachers, Academic subject teachers, and staff for Administration, Operations & Student Welfare). We surely have at least 100 other very good people to also thank for their wonderful support to the school ♥

I also had many other ideas in mind when, just a couple of days ago, I sent out the fun, open-ended, thought-provoking question, why do I write that “MATHS IS 183“?

Here in Blog Post #143, it’s fitting that 1 funny ‘Big Brother’ + 4 other teachers + 3 students will be starring with the creative answers that they sent in before I started writing this article 😊♥😊. Further down, I’ll offer my personal first idea, and some other still quite nice ones.

This kind of Maths can be very refreshing, because practically any idea from thoughtful children or adults is interesting to hear and to reflect on. There is certainly not just one ‘right answer’; the truth is that the good possibilities are infinite!

Guillaume is the school’s youngest current student, yet he was thinking until late yesterday evening, when he sent me his ‘answer’… Guillaume wanted MATHS to become a product M x A x T x H x S, with 183 as the target result. He realised very maturely that he could, for example, freely pick any non-zero number values for four of the five letters in MATHS, then calculate their product, after which the value of the one remaining letter would have to be 183 ÷ the calculated product. Guillaume liked the choice of starting with the whole numbers 1, 2, 3 and 5, after which the one other number value has to be 6.1, and it’s not far off being a whole number. His idea would work with an infinite number of different target numbers. Good thinking, Guillaume! Well done! 😊

Sophie noticed that the total number of characters in MATHS IS 183 is 5 + 2 + 3, or 10, and 3+8-1 also makes 10. Sophie’s idea there would work with lots of other numbers, too. Good job! 😊

Defne G. focused on 183 and wondered, had I turned 18 when I chose 3 as my favourite number?! I absolutely loved that thought 😊♥😊, and Defne was the only person to write in with the idea of splitting 183 into a two-digit number and a one-digit number. Especially at Christmas, I think of Joseph & Mary (two) doing their best to care for baby Jesus (the One to actually save everyone). You may ask, “Why particularly 18 and 3?”… An answer is coming soon…but apart from 183 in Maths, the Bible verse Matthew 18:3 is super-important: Jesus called a little child to His side and set him on his feet in the middle of them all. “Believe me,” He said, “unless you change your whole outlook and become like little children, you will never enter the Kingdom of Heaven. It is the man who can be as humble as this little child who is greatest in the Kingdom of Heaven.”

My ‘Big Brother’ Jan V.L. knows that 3 is my absolute favourite number, and Jens (another excellent colleague) remembered that I’m due to turn 61 on my next birthday. 183=3 x 61. Also, 3+6+1=10 & 1+0=1→”MATHS IS NUMBER ONE”! 😊 (Jens is actually a brilliant physicist, chemist and mathematician. We’ll hear of him again when I publish my solutions to Blog Post #142 in the coming days. Also, I’m intending to feature a beautiful brainteaser within Blog Post #144, soon 😊)

The Headmistress and Kate and David (also lovely colleagues at MMS) had essentially the same idea as each other, and the following words are from Kate:

“If you add the number of the position of each letter of the alphabet of the word MATHS together it equals 61. Mr. Mo is our MATHS teacher and his favourite number is 3. If you multiply 61 by 3, you get 183.”

(13 + 1 + 20 + 8 + 19) x 3 = 61 x 3 = 183.

Those are certainly fun ideas, but several of the adults quite rightly felt that there ought to be more than that to MATHS IS 183. After all, Galileo famously said, “Mathematics is the language with which God created the Universe.”

183 is a bit special because it’s actually the smallest positive whole number such that it, when concatenated with its next big brother 184, makes a perfect square number: 183184 = 428 squared. That’s a cute detail too, but still, is it really of significance at Christmas?

David (already mentioned above) was the very first to write in, and with two distinctly different ideas. His second one is particularly nice ♥♥♥

1 represents the Oneness of God

8 represents the Infiniteness of God

3–in Music, the ‘musical third’ is the interval symbolising Love = God

Paul & David on a school outing in 2021 😊😊

Personally, my principal idea was the following… Remembering that Maths is actually a universal language, instead of replacing letters by numbers…we can alternatively replace numbers by letters. I told you that I really liked Defne’s thought of seeing 183 as 18 3. Then, MATHS IS 18 3 becomes MATHS IS R C…to wish you and everyone a very blessed, merry CHRISTMAS ♥♥♥

With lots of love and kindest wishes as always,

Paul M😊twani ♥♥♥

P.S.

  1. Everyone at the school who sent in a nice answer in time will receive a ‘thankyou’ prize on Monday 😊
  2. All MMS colleagues and students are very warmly appreciated, and so there will actually be something nice for everyone there on Monday ♥
  3. Thanks to Wout for one of his lovely new thoughts this evening, that MATHS can stand for Maths At The High School, and in reply I congratulate Wout on being a really great MMS of MMS = Marvelous Mathematical Student of Musica Mundi School! 😊

Blog Post #142: Good Knowledge ♥

Dear Readers,

Theodore Roosevelt famously said, “A thorough knowledge of The Bible is worth more than a college education”, and I’m certain that he was right. Personally, I’ll always be truly grateful for all my excellent teachers of Mathematics, Physics, Chess, and many other fascinating subjects, but it’s still much more important to come to know God’s Word well through The Bible, which contains all the examples, truths, and commands that God wants us to know, believe, respect, and live by. In prayer, we can ask God to grant us increased understanding, wisdom and good powers of discernment. Mark 12:30 gives a clear, unmistakable message: “Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength.”

There are many people who want to have faith in God, but may be struggling with doubts. Three lines below here, there follows a free link directly to a really helpful recent article by Rev. John Piper (the founder of http://www.desiringgod.org)→

https://www.desiringgod.org/messages/the-purposes-of-god-in-the-pain-of-the-world

It’s well worth thinking about that article carefully. The good author has done a superb job of helping to answer questions which have troubled billions of people in the past, right up to the present time.

I am also thankful for every moment I have as the Mathematics teacher at Musica Mundi School (MMS), where I have the privilege and pleasure of working with wonderful students and colleagues. Since many of them enjoy puzzles, I will do my best to offer a bumper-sized gala feast now near Christmas! ♥😊♥

First, rearrange the letters of now King to make a proper seven-letter English word.

Also, rearrange the letters of xy gala to make a proper six-letter English word.

Next, here comes a wee joke… What might someone say if he/she didn’t know the meaning of the word ‘AXON’ in Biology?…”It’s getting on my nerves!!” 😊

Thinking of miracles performed by Jesus, use the letters of GLORY HEAL AXON to make OR + a proper 11-letter Maths-related English adverb. There’s a clue in the lovely photo just below…

Damla & Sophie are talented, young mathematicians, as is Valentin (pictured in the next photo).

Valentin’s eraser shows a famous image of Wolfgang Amadeus Mozart.
Mozart’s birthday was 27 January, which brings to mind the three-digit number 271.
Quick Puzzle: Can you read my mind and say why I’m also thinking of 2 x 71 now!?

Just before we meet more puzzles, I’d like to share a happy, musical memory with you… One evening in the school a couple of years ago, I was sitting doing Maths work in the dining hall, while simultaneously enjoying listening to a beautiful music album. A Turkish student named Idil (a fabulous cellist) came into the hall and immediately asked about the lovely album. She liked it so much that I sent her a link to the full album, right away. I think that it’s perfect for Christmas, and so I’m sharing it now with you, too! 😊♥😊

Duration: Just under 44 minutes. Happy listening!

I would also like to take this opportunity to wish all MMS students lots of enjoyment and success in all the concerts in which they are performing during this wonderful, festive period ♥

Musica Mundi School concerts are a delight to all who experience them ♥

Meanwhile, more puzzles are coming in fast now!

Imagine that a lady once declared on a weekday, “I know that I was working 142 days ago because it was a weekday back then. My birthday is 142 days from now, and that will also be a weekday; not during a weekend.”

Your fun challenge puzzle is to figure out what day of the week the lady’s birthday was going to be on. Also, on what day of the week did the lady make her statement?

Next, can you think of seventy-one consecutive integers which have a total sum of 142 ?

Here comes another interesting puzzle… The total sum of all the prime numbers less than N is a whole multiple of 71. If the prime number N is included too, then the new total sum is also a proper multiple of 71. Exactly what number is N ?

And now I’ll share a very short, true story with you… Just a few days ago, while driving on my way to work, I found myself behind a vehicle with a number plate that included 2 ♥ 7 1, where ♥ stands for a particular digit. Given the value of ♥ that I saw, I realised that the four-digit number 2 ♥ 7 1 must be a proper multiple of 99. Your fun challenge is to figure out the value of ♥. Also, in general, if ABCD is a proper multiple of 99, then what is the special connection between AB and CD ? (One exception to the general rule is 9999, in which AB = 99 = CD.)

BRAINTEASER

Imagine that XYZ stands for a proper three-digit whole number.

  1. Prove that XYZ times 3 can never equal YZX.
  2. Find two solutions to the equation XYZ times 3 equals YZW, where the only restriction is that W does not equal X.
It’s time now for a Chess puzzle to delight Timothée, Raphaël, and other fans of the Royal Game ♥
Black would love to queen the g-pawn, but…
right now it’s White to play and force checkmate in just three moves! ♥

By the way, let’s call Raphaël’s favourite whole number R. It’s a single-digit number. Here in blog post #142, it’s nice that 1 ÷ R gives the recurring decimal 0.142857142857… Also, 2 ÷ R or 3 ÷ R or 4 ÷ R or 5 ÷ R or 6 ÷ R all produce decimals with exactly the same recurring digits, in different orders. If you’ve already figured out the value of R, then it will only take an extra moment to figure out the date this month of Headmaster Herman’s birthday, coming in R+1 days from now 😊

Here’s sending early good wishes for Headmaster Herman
whose birthday is coming in R+1 days from now 😊

It’s my hope and intention (God-willing as always) to publish solutions to the puzzles around the time of the next blog post. In the meantime, please do feel free to send in your best solutions to some/all of the puzzles, if you like 😊

My family and I would like to wish you and everyone a very blessed, merry Christmas and a happy New Year, coming soon ♥😊♥

Jesus said, “In My Father’s house are many rooms. If that were not so, I would have told you, because I am going there to prepare a place for you.” John 14:2

We don’t have to wait until Easter–or even until Christmas–
to stop and recognise with gratitude Jesus’ sacrifice to save us all ♥
“For God so loved the world that He gave His one and only Son,
that whoever believes in Him shall not perish but have eternal life”– John 3:16.

With love and kindest wishes as always,

Paul M😊twani ♥

P.S. = Puzzle Solutions (being posted on 30.12.2022)

now King = Knowing

xy gala = galaxy

GLORY HEAL AXON = OR + HEXAGONALLY

2 x 71 = 142, the number of this blog post

142 days = 20 weeks + 2 days, so the lady was speaking on a Wednesday, looking forward to her birthday to come on a Friday (20 weeks + 2 days later), while also thinking back to a Monday when she was working, 20 weeks + 2 days earlier

The seventy-one consecutive integers from -33 to 37 have a total sum of 71 x the number at the very middle of the long list of numbers = 71 x 2 = 142, as required 😊

The prime number N = 71

♥ = 8; 2871 = 99 x 29; note that 28 + 71 = 99, and in general AB + CD = 99 when ABCD is a multiple of 99 (except in the case of 9999)

Consideration of the place values of the digits in XYZ shows that XYZ = 100X + 10Y + Z, while YZX = 100Y + 10Z + X;

it’s not possible that 3(100X + 10Y + Z) = 100Y + 10Z + X because that would imply that 300X + 30Y + 3Z = 100Y + 10Z + X, leading to 299X = 70Y + 7Z, which is a clear contradiction since 70Y + 7Z = 7(10Y + Z), a multiple of 7, but 299 is not a multiple of 7 and if X=7 then 299X = 299 x 7 = 2093 which is far too big to equal 70Y + 7Z, given that digits Y & Z can’t be bigger than 9; so the proof is complete 😊

In part 2 of the brainteaser, the requirement boils down to

300X – W = 7(10Y + Z);

if X = 1 & W = 6, then 300X – W = 300 – 6 = 294 = 7 x 42, a multiple of 7, so we’ve found that it works with 3 x 142 = 426;

similarly, if X = 2 & W = 5, then 300X – W = 600 – 5 = 595 = 7 x 85, a multiple of 7, so we’ve also found that it works with 3 x 285 = 855;

there are no higher solutions, because if X = 3 or more, then 300X – W would be far too big to equal 7(10Y + Z), given that digits Y & Z can’t be bigger than 9 😊

In the chess puzzle, White forces checkmate with 1 b6! cxb6 2 a7 followed by 3 a8=Q#, and ‘underpromoting’ to a rook at the end is also perfectly sufficient 😊

Raphaël’s favourite number is R=7

Headmaster Herman’s birthday came on December 20, which was 7+1 days after this blog post was first published (on December 12) ♥

Blog Post #141: Christmas Celebration of Love ♥

Dear Readers,

Christmas (no less than any other time) offers you, me, and the whole world a perfect opportunity to recognise clearly, and celebrate with joy and thanks, God’s perfect love for us in having sent ♥ Jesus as the one true Saviour ♥ that we all need if we are to go to Heaven after our short lives now. In comparison to that all-important truth, I realise that anything that I might know about Mathematics, Chess, or other subjects, is practically insignificant.

Still, God purposely gave us all personal gifts to be used well, and so I will now offer some beautiful puzzles which I hope that many readers will enjoy solving.

The first puzzle (below) is one that I thought of just yesterday, and of all the puzzles that I have ever offered, it’s definitely one of my absolute favourites.

♥ Christmas Love Celebration Brainteaser ♥

In the Addition Pyramid, each of the letters
C, H, R, I, S, T, M, A, L, O, V, E–and also the red heart–stand for numbers.
The number 52 is the number of complete weeks in a year,
while 31 is the number of days in the Christmas month of December ♥

Your Christmas Love brainteaser challenge is this: If the total sum of all the fifteen number values (for C, H, R, I, S, T, M, A, L, O, V, E, and also 52, 31 and the red heart) equals 141, then what must be the exact number value of the red heart?

NOTE WELL: Each item anywhere above the bottom row of the pyramid always equals the sum of the two items just below it. For example, I = M + A, because M & A are just under the letter I there. Similarly, R = S + T, and so on.

The number 141 has specially appeared in my life on literally hundreds of occasions within my sixty years, so far, and I couldn’t help noticing that the total sum of the eleven numbers in the display column of the next photo (here in blog post #141) is again 141 😊

♥ A Second Lovely Puzzle ♥

From the display board, I’m thinking of two particular numbers. If I increase the numbers by 10 each, their product increases by 300. What are my two starting numbers?

The word ‘CARDS’ may be closely connected to ‘CARES’, and ‘REASON’ is certainly connected to ‘SEASON’ through the perfect truth given in the next photo ♥

♥ A Wonderful Chess Study ♥

Despite being two pawns down, it’s White to play and win by force
in this wonderful old chess study by H.Rinck ♥

It’s now 22 days until Christmas 2022. Sometime before then, I hope and intend (God-willing, as always) to publish solutions to the puzzles within this post, but please do feel free to send me your best solutions to any/all of the puzzles, if you like 😊

Here’s a beautiful detail regarding the birthday tomorrow (4 December, 21 days before Christmas) of a lady I know, born in 1965… I shared with her that 21 x 1965 = 41265. We noted that, even I were just to write 21 x 19XY = D12XY, it can be proven that the day number D has to be 4 and the year has to be 1965; that’s the unique solution ♥

To everyone whose birthday is yet to come this month, I wish you a wonderful, happy time. Most of all, I wish everyone a very blessed Christmas soon.

With love and kindest wishes as always,

Paul M😊twani ♥

P.S. = Puzzle Solutions (being published now on 12.12.2022)

The Addition Pyramid Brainteaser can actually be solved rather quickly by considering the sums of the entries, one row at a time…

Top Row: 52

2nd Row: 52

(because C + H must exactly match the number 52 positioned right above the letters C & H)

3rd Row: 52 – ♥

(because R + ♥ + I = (R + ♥) + (♥ + I) – ♥ = C + H – ♥ = 52 – ♥)

4th Row: 52 – ♥ – ♥

(because S + T + M + A = (S + T) + (M + A) = R + I = (R + ♥ + I) – ♥ = (52 – ♥) – ♥)

Bottom Row: 52 – ♥ – ♥ – ♥ + 31

(because L + O + 31 + V + E = (L + O) + (V + E) + 31 = S + A + 31 = (S + T + M + A) – (T + M) + 31 = (52 – ♥ – ♥) – ♥ + 31)

So, the grand total sum of all the rows is

52 + 52 + 52 – ♥ + 52 – ♥ – ♥ + 52 – ♥ – ♥ – ♥ + 31 = 141 (given information)

→(52 x 5) -6 x ♥ + 31 = 141

→260 – 6 x ♥ + 31 = 141

→291 – 6 x ♥ = 141

→6 x ♥ = 150

→♥ = 150 ÷ 6 = 25.

♥ = 25, perfect for Christmas 😊

In the second puzzle, suppose that X & Y represent the two numbers that I was thinking of. Then, from the information given in the puzzle,

(X+10)*(Y+10)=X*Y+300

→X*Y+10*X+10*Y+100=X*Y+300

→10*X+10*Y+100=300 (after cancelling X*Y terms)

→10*X+10*Y=200

→X+Y=20 (after ÷ by 10)

The only numbers on the display board which could satisfy the requirement X+Y=20 were 9 & 11.

Warm congratulations to Jens Van Steerteghem, who solved that puzzle and the Addition Pyramid ♥ Brainteaser! 😊♥😊

In the Chess study, White wins with 1 c4! (threatening 2 Qd5#) 1…Qe4 2 d4+!, after which either 2…cxd4 or 2…Qxd4 is met by 3 Qe7#.

Alternatively, 1 c4! Qh1 2 d4+! cxd4 3 Qe7#, or 2…Ke4 and Black’s queen will be lost after the skewering check 3 Qd5+.