Blog Post #152: A Good Heart πŸ’–

Dear All,

This article is specially dedicated to Dr. Vipin Zamvar, a consultant cardiothoracic surgeon who certainly has a really good heart, in the kindest, very best sense ❀. Vipin is originally from Mumbai, India, but now lives in Edinburgh, and my family and I had the pleasure of meeting the gentleman doctor in Scotland’s beautiful capital city through an event at Edinburgh Chess Club last October. We thoroughly enjoyed chatting with Vipin during dinner that evening, and when he kindly gave us a lift to our hotel afterwards. In addition to sharing the ‘Royal Game’ of Chess as a fine hobby, we also like Mathematics, and I am currently reading ‘The Music of the Primes’ which Vipin sent as a lovely gift book.

I would like to now offer several fresh brainteasers for the enjoyment of Vipin and all puzzle fans! 😊❀😊

  1. Start with the number 152 here in Blog Post #152.

Multiply it by my favourite number, 3, and then add 3.

If you divide the result by Vipin’s favourite whole number, you’ll then have a prime number.

What exactly is Vipin’s favourite whole number (given that it is not more than 152) ?

2. Rearrange the letters of CREMONA (a beautiful city in Italy) to make a proper 7-letter English word. The nice seven-letter word – – – – – – – has a connection to Vipin because he chose his favourite number for the reason that it was part of the date on which he first met his wife ❀

What a lovely couple! We see Vipin and his wife, Usha, pictured in Coimbatore, India πŸ’–πŸ’–

3. We already encountered the number 459 in the first puzzle (when doing 152 x 3 + 3), and now imagine that Vipin selects either 4 or 5 or 9. Let’s call his selected number V. Vipin will raise V to the power of his wife’s age now, and he’ll note the result. Vipin will also raise V to the power of his wife’s future age on her next birthday, and again he’ll note the result. Vipin will add his two results together to get a new, larger result, Z.

What exactly will be the units (or ‘ones’) digit of the number Z?

Can you prove what the digit will be?

4. Imagine a long bus travelling at a constant speed through a tunnel in India that is nearly 1km long. (The tunnel length is in fact a whole number of metres between 900 and 1000. The length of the bus is also a whole number of metres.) From the moment that the front of the bus enters the tunnel, the time taken for the entire bus to be inside the tunnel is t seconds. However, the time taken for the entire bus to pass through the tunnel is t minutes.

What is the exact length of the tunnel?

5. Now it’s time for an ABCD puzzle to wish you A Beautiful Creative Day!


The diagram shows two overlapping circles of equal radii, r, say. The points A, B, C and D are collinear, and all lie on the line which passes through the centres of the circles.

If BC is not less than AB + CD,


what is the maximum-possible value for AD Γ· r ?

6. People don’t normally like going round in circles, but still…

…this next puzzle is actually lots of fun, too!! πŸ˜‚

Imagine that the distinct positive whole numbers 2, 3, 4, 5, 6 and X are going to be placed in the six rings; one number per ring. The products of the numbers on each of the three edges of the triangular array are to be equal to each other, and will each be P, say.

What is the value of X?

Also, what is the maximum-possible value for P?

7. In Chess, Vipin and I both like playing the Caro-Kann Defence as Black. So, let’s now enjoy seeing it in action in a super-fast victory 😎 from Kiev in 1965, the year when Vipin was born. πŸ’–

Mnatsakanian vs. Simagin, Kiev 1965.

1 e4 c6 2 Nc3 d5 3 d4 dxe4 4 Nxe4 Nf6 5 Nxf6+ exf6 6 Bc4 (6 c3 followed by Bd3 is more popular nowadays) 6…Be7 (Several decades ago, super-GM Julian Hodgson told me that he likes 6…Qe7+, especially if White responds with 7 Be3?? or 7 Ne2?? which lose to 7…Qb4+! 😁) 7 Qh5 0-0 8 Ne2 g6 9 Qh6 Bf5 10 Bb3 c5 11 Be3 Nc6 12 0-0-0? (White’s king castles into an unsafe region where it will be attacked very quickly indeed…) 12…c4!! 13 Bxc4 Nb4 14 Bb3 Rc8 (the point of Black’s energetic pawn-sacrifice at move 12 has become clear along the opened c-file) 15 Nc3 Qa5 (also good is 15…b5, intending 16 a3 Rxc3!! 17 bxc3 Nd5 with an enduring attack for Black in addition to having enormous positional compensation for the sacrificed material) 16 Kb1? (It’s often difficult to defend well against a sudden attack, but this move simply loses by force; 16 Bd2 is more tenacious)

Get ready for a beautiful Chess combination! 😍

16…Rxc3! (16…Bxc2+! 17 Bxc2 Rxc3 also works) 17 bxc3 Bxc2+! 0:1. White resigned, in view of 18 Bxc2 Qxa2+ 19 Kc1 Qxc2# or 18 Kc1 Nxa2+ with decisive threats against the fatally exposed White monarch.

I’m pretty sure that Scott Fleming (who recently sent me a really nice letter from Arbroath, Scotland) will also enjoy that very neat, crisp win for Black, as will FIDE Master Craig SM Thomson, who has played lots of wonderful games with the Caro-Kann Defence for nearly 50 years already!! πŸ‘πŸ˜Š

It’s my intention to publish solutions to all the puzzles around the time that blog post #153 comes out, God-willing as always.

In the meantime, please do feel free to send me your best solutions to any or all of the puzzles, if you like 😊.

I would like to round off this article now by most sincerely wishing you a very blessed weekend, with lots of happiness in everything that you do ❀.

Special congratulations to my friend James Pitts who has turned 53 today.


With kindest wishes as always,

Paul M😊twani ❀

“He has dethroned rulers and has exalted humble people.”

–Bible verse, Luke 1:52 β™₯

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 My e-mail address is You can find me on Facebook, too.

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