Blog Post #86: For Three Good Friends: Jacques, Peter and Annabel xxx

Dear Readers,

Jacques, Peter and Annabel (three very good colleagues and friends of mine) all featured nicely in Blog Post #85. Through the puzzles there, we learned that their respective best-loved numbers are: 7, 13 and 19.

Today, I am thinking of another ‘secret whole number’…

Suppose that Peter multiplies his 13 by my secret number and notes the result.

Annabel also multiplies her 19 by my secret number and notes the result.

Jacques also multiplies his 7 by my secret number and notes the result.

They then add up their three results together and…

the total equals the year when a really famous German composer was born!

(However, this time it’s not Ludwig van Beethoven!)

My three-part mathematical Music brainteaser for you is this:

  1. Who is the really famous German composer that I am thinking of?
  2. What was his year of birth?
  3. What is my exact ‘secret whole number’ mentioned at the start of this puzzle?

I could sincerely TELL OF RESEARCHING

that I did to ensure a good solution to this intriguing puzzle, or I could simply add now that the three capitalized words just above also make ORCHESTRAL FEELING ! (See Blog Post #85: Orchestral Feeling.)

Wishing you lots of fun and a wonderful weekend now,

Paul Motwani xxx 

P.S.=Puzzle Solution!

This will be published later because, in the meantime, my colleagues and the students at Musica Mundi School, as well as other students whom I work with personally, can win great prizes if they email high-quality solutions to me.

SOLUTION (being posted now on 31.1.2021)

When Peter multiplies his favourite number, 13, by my secret number, N, his result will be 13 x N, which is usually shortened to 13N. Similarly, Annabel will get 19N, and Jacques will get 7N.

The grand total is 13N+19N+7N, which equals 39N. Therefore, the total must be an exact multiple of 39, and that is the main key to unlocking the solution.

Now, what is the exact value of N? Well, if N=43, for example, then 39N=39 x 43 =1677; just eight years too early for the birth of Germany’s Johann Sebastian Bach.

Trying N=45 leads to 39N=39 x 45 = 1755, just fifteen years too early for the birth of Germany’s Ludwig van Beethoven.

However, with N=47 it’s B for ‘Bingo!’ and for Germany’s Johannes Brahms

(1833-1897) because 39 x 47 = 1833.

So, a solution involving a really famous male German composer has certainly been found, but couldn’t there be other solutions…!?

Well, among literally hundreds of celebrated German composers listed at https://en.wikipedia.org/wiki/List_of_German_composers

I could find only five who were born in years that are exact multiples of 39.

The famous five* are:- (I’ll try to count well now! )

Johann Ludwig Bach (born in 1677=39 x 43;

NOT to be confused with Johann Sebastian Bach born in 1685 !)

Caspar Joseph Brambach, Franz Wohlfahrt and Johannes Brahms who were all born in 1833=39 x 47.

All of them were surely wonderful musicians. Brahms was the first one I thought of, partly because his unforgettable music has been referred to on several occasions in nice conversations with David Baltuch, one of Musica Mundi School’s great Music teachers.

* I can almost hear some of you yelling, “Just hold on a sec., Mr. Mo! You only gave us four composers!”

Yes, part 2 of the puzzle had asked, “What was his year of birth?”, but I did also find a very special female German composer born in 1794=39 x 46.

She is Princess Amalia Auguste. Her full name is really long, not with 26 letters…but with 126 letters altogether!

Maria Amalia Friedericke Augusta Karolina Ludovica Josepha Aloysia Anna Nepomucena Philippina Vincentia Franziska de Paula Franziska de Chantal !

It’s quite fitting that the prize-puzzle winner is female! She’s Louise, a very clever student of mine who will be enjoying a well-deserved delicious German Black Forest cake!

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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