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) ♥

Author: Paul A. Motwani

My name is Paul Motwani, but my colleagues, my students and their parents mostly call me "Mr. Mo"! My middle initial, A, stands for Anthony, because I was born on the official feast day of St. Anthony of Padua, the patron saint of miracles and of lost souls. I love teaching Mathematics and Chess, and giving fun-packed talks and shows in schools and clubs. The popular ingredients of Math, Chess, Mystery and Magic are my "Fantastic Four", and I give prizes too! I am an International Chess Grandmaster, and (loooooong ago!) I was the World Under-17 Champion. I am the author of five published chess books and hundreds of newspaper articles. I live with my wonderful wife and son in Belgium. I also love music, movies and puzzles. I blog at paulmotwani.com. My e-mail address is pmotwani141@gmail.com. You can find me on Facebook, too.

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