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 ♥😊😊♥
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 ♥😊♥
Early Birthday Puzzle about Anuurai ♥
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 ♥😊♥
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.
Raphaël is one of the very bright and talented, young mathematicians who also loves chess at the school ♥
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 & winIt’s White to play & win by force in this elegant study by A.TroitskyIt’s Black to play & win quicklyIt’s White to play & win in this early birthday chess treat for Anuurai (which is actually a study from almost 136 years ago!!) ♥
Have a wonderful day, dear friends, and keep a smile on your face and a rainbow in your heart ♥😊♥
With kindest wishes as always,
Paul M😊twani ♥
P.S. = Puzzle Solutions
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.
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.
Black wins quickly with 1…exf2++ 2 Kxf2 (or 2 Kd2 Qe1+ 3 Kc2 fxg1=Q) 2…Qe1+ 3 Kf3 Qg3#.
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! ♥
“May the God of hope fill you with all joy and peace in believing, so that by the power of the Holy Spirit you may abound in hope.” Romans 15:13
“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 ÷ 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 ÷ 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 ♥😊♥
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! ♥😊♥
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 ♥
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# ! ♥😊♥
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
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 ♥
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 ♥
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!” ♥😊♥Hagit & Leonid’s blossoming school brings beautiful music to many ears ♥
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 !
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! ♥😊😊♥
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 eachof 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 ♥ 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! ♥😊♥
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 ♥😊😊♥
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 ♥😊♥I intend to publish solutions on Sunday, when Leonid turns 60 ♥
In the meantime, I wish everyone lots of love, blessings and a very happy weekend ♥😊♥
With kindest wishes as always,
Paul M😊twani ♥
“Every good gift and every perfect gift is from above, coming down from the Father” James 1:17
Faithful friends are gifts from Heaven ♥
Joke: What would Winnie the Pooh get by crossing Piglet with a violin?
Hamstrings!!
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) ÷ 84 = 84. That’s the only solution with positive whole numbers to the equation (y – 13)(y + 13) ÷ 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#.
Paul Motwani 