Blog Post #100: A Priceless Gift of Love for Easter

Dear Friends,

No securer intro. is possible than to say honestly and happily that I am celebrating with gratitude an event which can be discovered by rearranging the letters of OUR CENTRE SIR (or of securer intro).

The true message of Easter celebrates the RESURRECTION of Jesus, triumphing over death and marking the beginning of a new covenant between God and people, through which everyone who believes will enjoy eternal life.

The Good News Translation of John 3:16 in The Bible is: “For God loved the world so much that He gave His only Son, so that everyone who believes in Him may not die but have eternal life.”

That is really clear and wonderful news for everyone who will simply recognise and accept with sincere thanks the priceless gift.

The most important news has rightly been shared first.

I do have a lovely, fresh puzzle to offer now, too.

It involves a true story about 12 people who are all either students or colleagues of mine at the magical Musica Mundi School in Waterloo, Belgium. (Some of them are pictured in this article.)

I asked each person to pick his/her absolute favourite number. The 12 people picked 7, 8, 9, 11, 13, 16, 19.

As only seven different numbers were picked by the 12 people, we can realise that some people must have picked the same number as each other.

I will now add a couple of very significant extra facts. The numbers 7, 8 and 9 were all equally popular. Also, the grand total sum of the 12 people’s numbers was 133.

Your fun brainteaser is to figure out precisely how many people picked each of the listed numbers 7, 8, 9, 11, 13, 16, 19.

I hope to be back in person at the school on 19 April, and on that day I would love to award a special prize to the student(s) and/or colleague(s) who might send me good solutions by email before this coming Easter Monday, 5 April. Aim high, dear friends!

Aiming High towards Heaven

In the meantime, please enjoy a delightful selection of photos which shows some of the Musica Mundi School Family almost literally reaching for the sky!

God-willing as always, a full solution to the brainteaser prize puzzle will be published at the time of the next blog post, or possibly even sooner.

Update being posted now on Easter Monday, 5 April 2021

Special congratulations to Elaine G., a dear Scottish friend who solved the brainteaser. A scrumptious Easter gift is already on its way to Elaine’s home in Edinburgh.

Easter Eggs for Elaine!

Here is a complete, clear, step-by-step method for finding the unique solution to the brainteaser.

Step 1: The sum of the seven numbers 7, 8, 9, 11, 13, 16, 19 is 7 + 8 + 9 + 11 + 13 + 16 + 19 = 83. That would be the total if each of the seven numbers occurred just once each, picked by seven people.

Step 2: The grand total sum of 133 (for 12 people’s numbers) was included in the info. given in the puzzle, and is 50 more than 83. So, five people’s numbers must have a total sum of 50.

Step 3: At least one of those five people’s numbers must be 9 or less, since if they were all 11 or more, then their total would be greater than 50.

Step 4: However, we were also given (in the info. with the puzzle) that the “numbers 7, 8 and 9 were all equally popular.” So, since we know (from Step 3) that at least one of the numbers 7, 8, 9 must occur twice, it follows that all three of them occur twice, in order to be “equally popular.” (Note that 7, 8, 9 cannot occur three times each, together with 11, 13, 16, 19 at least once each, because that would take more than 12 people to have picked the numbers!)

Step 5: Having established that ten of the 12 people must have picked 7, 7, 8, 8, 9, 9, 11, 13, 16, 19, the total sum so far is 107. To reach the final target of 133, the remaining two people’s numbers must total 26, and must be from 11, 13, 16, 19, since we already know that none of 7, 8, 9 can feature a third time. The only way to finish the job correctly is with 13, 13 for the ‘missing’ two numbers.

In summary, the solution is: 7, 7, 8, 8, 9, 9, 11, 13, 13, 13, 16, 19.

In her email to me several hours ago, Elaine presented her solution succinctly and prettily like this:

1 x 11 16 19  = 46

2 x  7  8  9    = 48

3 x  13            = 39

                          – – – – 

                           133 👌

Elaine has sometimes said that Maths is not really her thing, but it’s great that she was willing and not afraid to have a good go at the brainteaser…and she succeeded in style! Congratulations again!

Blog Post #101 is very likely to include an original chess brainteaser that I composed recently…

Right now, though, I would like to wish everyone a wonderful, happy weekend.

With kindest wishes as always,

Paul Motwani xxx

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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