Blog Post #41: We Can All Be Winners

Dear Readers,

Hello again, and welcome to my 41st blog post. With my first 40 posts, I happily started a tiny tree, and now to start off today I have a quick puzzle coming for you!

TINY TREE

Make a proper eight-letter English word using all the letters of TINY TREE.

Congratulations if you realised that TINY TREE gives ETERNITY, and special congratulations if you totally solved the puzzle by thinking of ENTIRETY, too!

Good News

I believe that you and I each have one life now to later become happy winners with God for eternity. The really good news is that EVERYONE who believes in God and loves His people will enjoy eternity with Him. We only have to accept the happy truth, and care enough to pass on the good news to others.

The words “…my only aim is to finish the race and complete the task the Lord Jesus has given me–the task of testifying to the good news of God’s grace”, from Acts 20:24 in The Bible, were surely an inspiration for Eric Henry Liddell (1902-1945), the ‘Flying Scotsman’ athlete and missionary whose life story formed a great part of the 1981 Academy Awards-winning film, “Chariots of Fire”. Eric Liddell won the gold medal in the Men’s 400m race at the 1924 Paris Olympics. A long time afterwards, when Scotland’s Allan Wells won gold in the 100m sprint at the 1980 Moscow Olympics, he dedicated his victory to the memory of Eric Liddell.

Eric Henry Liddell, The Flying Scotsman

When Eric Liddell won his Olympic gold medal, his T-shirt had the number 451 on it.

Me, pictured beside a little memorial to Eric Liddell in St. Andrews, Scotland, on 25 July 2016.

Eric Liddell Challenge!

Can you find two whole numbers, both greater (bigger) than 1, which can be multiplied together to give the number 451 on Eric Liddell’s T-shirt?

Solution to the Eric Liddell Challenge

Fittingly in this Blog Post #41, the unique solution to the puzzle is: 11×41=451. A handy fact to note about three-digit numbers is that they are always multiples of 11 if the sum of the first and third digits is either equal to the middle digit or differs from it by any multiple of 11. For example, in the case of 451, the fact that 4+1=5 guarantees that 451 is a multiple of 11. Quick bonus: What is the first multiple of 11 that is more than 400…? The answer is 407, because 4+7=0+11. For the record, 407=11×37.

MATE IN 4 ON APRIL 4TH!

It is White to move and force checkmate in at most 4 moves.

To celebrate Easter, I offered a nice prize (a surprise!) to whoever might send me what I would consider to be the very best, well-explained solution to the brainteaser puzzles that were published on March 26th in Blog Post #40.

I am delighted to announce now that Mr. Gerald Schmidt and his family will soon be receiving a very large and delicious collection of Lindt chocolates that my wife bought yesterday for them. Warm congratulations to the whole Schmidt Family.

Mmmm…yummy!

For convenience, I will give again now the full brainteaser info. & details that I published in Blog Post #40, so that it will be much easier to follow the solutions being published today.

Published on 26 March: “Earlier today, I messaged Jane and Alex, friends who have their birthdays tomorrow. I also thought of Julia, a friend and former colleague whose birthday is on the same day as that of David, a retired minister who is the father of another friend and former colleague! Last, but certainly not least, I remembered Ingrid–a friend whose birthday is actually before Julia and David’s birthday–and I will contact Peter and Yen whose birthdays are later. There are so many happy birthdays to celebrate that we almost need 32 days in the month!”

BIRTHDAY BRAINTEASER #1

If I multiply together the March birthday day numbers of David, Ingrid and Julia, and then divide by 32, I still get a whole number result. Your fun brainteaser is to figure out that whole number precisely, and the March birthday day numbers of Ingrid, David and Julia.

The brainteaser can be completely solved using only the information given in this article.

BIRTHDAY BRAINTEASER #2

Suppose that Jane and Alex were to multiply their new ages together tomorrow and then add on both of their new ages. Subtract that result from the product of their ages next year (on their birthdays on 27 March 2019). What is the final result?

BRAINTEASER SOLUTIONS

  1. At the time the brainteasers were published, the only day numbers remaining in the month were March 26, 27, 28, 29, 30 and 31. Note particularly that 28 is the only multiple of 4 available there, and 26 is the only earlier multiple of 2 available there. No multiples of 8 were available. Now, since 32=2x2x2x2x2=2x4x4, we’ll only be able to get a proper multiple of 32 from the product of Ingrid’s, David’s and Julia’s birthdays if we match them to precise day numbers as follows:- Ingrid: March 26 (with birthday before David & Julia), David: March 28 & Julia: March 28. Then 26 x 28 x 28 ÷ 32=637.
  2. Suppose that J and A were the respective ages (in years) of Jane and Alex on their birthdays on 27 March, last week. On 27 March 2019, the new ages will be J+1 and A+1. Then (J+1) x (A+1) – (J x A + J + A)=J x A + J + A + 1 – J x A – J – A. Almost all the terms cancel; we are left only with 1, the final result.

SOLUTION TO MATE IN 4 ON APRIL 4TH!

1 f4! (threatening checkmate with 2 f5 or 2 h5) forces 1…h5, but White then wraps things up with 2 f5+ Kh6 3 Be3+ Rg5 4 Bxg5# or 4 hxg5#.

To finish this article, my family and I would like to wish everyone a very happy Easter.

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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