Blog Post #75: Turn Over A New Leaf

Dear Readers,

I first heard the saying ‘Turn over a new leaf’ as a little boy, long ago. I have found the words to be very good, refreshing, encouraging and helpful for making positive changes. I can’t think of a better day to seriously consider turning over a new leaf than on All Saints’ Day, today.

Almost every day, I hear beautiful, heart-warming music at Musica Mundi School where I work as the Mathematics teacher. Leonid Kerbel and David Baltuch-two of the school’s great Music teachers-feature in three of the following fun puzzles (which I first thought of months ago)!

Solutions are given near the end of this article.

  1. If I were to write
    and go on forever, which letter would be exactly the 1000th bold letter? It’s good to find a clear reason for your answer.
  2. Imagine a bag containing the six letters L, E, O, N, I, D; just one of each. I dip my hand in and randomly pull out four letters, one at a time. What fraction gives my chance (or probability) of getting the letters L,I,O,N in that order? 
  3. I am thinking of a very famous composer… It’s not Beethoven or Mahler…Instead, think ‘until – – – -.’ The answer is basically ‘in Baltuch’!
  4. A few weeks ago, I saw the following puzzle posted by chess friends on Facebook, and I liked it so much that I decided to share it here.       It’s White to play and force …checkmate in 8 moves!
  5. P.S.=Puzzle Solutions!                                                                                                             1. Since there are 19 letters altogether in HAPPYBIRTHDAYLEONID, and 19 x 52 =988, we’d then still have 12 more to go to reach the 1000th letter. The 12th letter in HAPPYBIRTHDAYLEONID is A, and so A is the answer.                  2. If I randomly pick four letters, one at a time, from L, E, O, N, I, D, then I basically have 6 possibilities for the first letter I could get; in each case, I’ll have 5 possibilities for the second letter; 4 possibilities for the third letter; 3 possibilities for the fourth letter. That produces a total of 6 x 5 x 4 x 3 = 360 different possibilities. Only one of those 360 permutations will comprise the letters L, I, O, N in that specific order. Therefore, my mathematical chance or probability of getting L, I, O, N is the fraction 1/360.                                                3. IN BALTUCH is an anagram of UNTIL BACH !                                                       4. White forces a beautiful checkmate as follows: 1. Kd4+! Rg2 2. Kd3! g5 3. Ke3 g4 4. Kf4 g3 5. Bf3! d5 6. Kg4 d4 7. Kxh3 d3 8. Bxg2#.
  6. To round off this article, my lovely wife, Jenny (who is sometimes a wee bit shy about posting photos), my son, Michael, and I do most sincerely wish you peace, joy, love and more xxx                                                                                        I dedicate this article to James Pitts (a very dear friend and colleague from my last school ), who has often talked with me about the                              Fruits of the Holy Spirit.

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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