Dear Readers,
A particularly beautiful Bible verse is “I give thanks to You, O Lord my God, with my whole heart, and I will glorify Your name forever”-Psalm 86:12. That verse is inspirational because it reminds us that we give glory to God by doing everything with gratitude to Him.
Earlier today, my son and I had a nice chat while I drove him to Brussels Zaventem Airport for a special weekend trip that he’s making. On my way back home afterwards, I spotted a vehicle with an interesting number plate which led me to making a fascinating investigation into properties of numbers. For me, it was like receiving a surprise gift. I’m going to share it with you now, and I wish you lots of enjoyment too ♥😊😊♥
I like my house number, 11, but my absolute favourite number is 3. So, I invite you to write down a three-digit number 11N in which N is any digit that you like from 0 to 9. Now calculate N x 11N, and let’s call the result your Star Number.
Next, we’ll shake things around a wee bit 😊 because I’m going to ask you to calculate 1N x 10N (where 1N is a two-digit number and 10N represents the three-digit number with digits 1, 0 and N). That new result will be your Super Star Number.
Question 1.1: What is the relationship between your Super Star Number and your Star Number?
If N is now any whole number (which can even be as big as you like), then N x (110 + N) is clearly not prime because it’s a product of numbers N & (110 + N). Even 1 x (110 + 1) is not prime because 1 x 111 = 111 = 3 x 37, a composite product.
Question 1.2: Is 1000 + N x (110 + N) prime or not?
Part of the license plate number that I saw today was 819.
Question 1.3: Can you show why 819 is a possible Star Number?
Question 1.4: Can you show why 1819 is a possible Super Star Number?
Here in Blog Post #138, let’s note that 138 = 2 x 3 x 23.
Question 1.5: 1819 raised to the power of P results in a 23-digit whole number. What is the value of P? Also, can you calculate the exact 23-digit result!?
Question 1.6: (138 x P ÷ 3) raised to the power of (3 x 3) also results in a 23-digit whole number. Can you calculate that 23-digit result precisely, too!?
Question 1.P: Can you spot a special connection between the 23-digit results of questions 1.5 and 1.6 ?
It’s my intention to wait a day or two before publishing solutions so that, in the meantime, readers can enjoy tussling with the puzzles. You are most welcome to send me any/all of your answers, if you like…and now I have more goodies for you!
My dad is not a chess player, but I think that he’ll like the fact that I’m now going to feature a truly fantastic old chess study from Germany (in which it’s White to move and force checkmate in 5 moves) in early celebration of his birthday coming up soon, on 5 December ♥😊♥
Question 1.8: By the way, how old will my dad be then (on 5 December) if I tell you that his new age + his age 38 years before then will equal 138 ?
Brilliant Old Chess Study from Germany (also shared recently by others on Facebook)
Early Christmas Word Puzzle ♥😊♥
Remove a particular letter from GERMANY and then rearrange the remaining six letters to make a proper 6-letter English word which relates to Christmas. There is just one, unique solution.
I will finish now by wishing you and everyone a wonderful, happy weekend.
With kindest wishes as always,
Paul M😊twani ♥
P.S. = Puzzle Solutions (being posted now on 13.11.22)
1.1 The Super Star Number is always exactly 1000 more than the Star Number.
1.2 Since 1000 + N x (110 + N) is actually the same as the product (10 + N) x (100 + N), it’s always composite; never prime.
1.3 819 = 7 x 117, and is therefore one possible Star Number (with N = 7).
1.4 1819 = 17 x 107, and is therefore one possible Super Star Number (also with N = 7).
1.5 P = 7, and 1819 raised to the power of 7 gives the 23-digit result 65891424018613967932339.
1.6 (138 x 7 ÷ 3) raised to the power of (3 x 3) gives the 23-digit result 37213699403613156884992.
1.7 It’s not so easy to spot at a glance that the two 23-digit results actually contain exactly the same 23 digits (in two different orders, of course) ! ♥
1.8 88 + (88 – 38) = 138. My dad will be turning 88 on his birthday next month ♥
Brilliant Old Chess Study Solution
The incredible, most powerful, centralising move for White from the chess study position given earlier is 1 Qe4!!, intending Qb1 followed by Qb5# or Qb6#.
while after 1…Rxe4 (or 1…Qxe4) 2 Rh8, Black cannot prevent 3 Rc8# !
Black sees that 2 Qb1 is threatened, and 1…Nd2 loses to 2 Qe3, for example.
My favourite variation in this stunning study is probably 1…Qf3 (to answer 2 Qb1? with 2…Qb3!) 2 Qd4!! Rxd4 3 Rh8 Be4 4 Rc8+ Kd5 5 Rc5# ♥😊♥
Another line is 1…Qg1 2 Qb1 Qc5 3 Qb4!! (even stronger than 3 Nxc5) 3…Qxb4 4 axb4 and 5 b5# cannot be stopped!
Early Christmas Word Puzzle Solution
GERMANY – Y gives GERMAN which rearranges nicely to make MANGER for Christmas coming soon ♥
Special congratulations to my friend and brilliant colleague, Jens Van Steerteghem (one of the Science teachers at Musica Mundi School), who sent in terrific answers to many of the mathematical puzzles. Feel free to now enjoy Blog Post #139: Yo, Jens! 😊😊
Paul Motwani 