Dear All,
The concept of ‘Parity’ is even more important in relation to people than it is with regard to whole numbers in Mathematics. Two numbers are of equal parity (no matter how big or small they are) if they are either both even or are both odd numbers, but all people are loved infinitely by God, our Creator, and so no-one is less important than anyone else. In that respect, we have parity (equal importance). Each person is unique, though, and I would like to very sincerely wish you lots of happiness and success in using your personal gifts to do as much good as you can. 💖
Puzzle: We awarded 1 point for a win, 0 for a loss, 0.5 to each player in the case of a draw. Five players are (at least) partly visible in the photo. Their total points awarded from the games pictured turned out to be 3 points.
What conclusion can you deduce from that information? 👍✔️
Wonderful Quotation: “To listen to the Word of God, listen with your ears and hear with your heart”–Pope Francis 💕
Word Puzzle: Rearrange the letters of PRAY IT to make a proper, six-letter English word.
Bonus Word Puzzle: Rearrange the letters of PREP HOW to make a seven-letter word.
Extra Bonus Word Puzzle!!: Rearrange the letters of FED MORE to make a seven-letter word. 👍😊
Two people I know well, who both have birthdays tomorrow, are Ask-Johannes (a Norwegian teenager) and Michael-Roy (the eldest son of Paul & Gill, very dear Scottish friends of mine). 💕
A Nice Numbers Happy Birthday Brainteaser for Tomorrow, 22 November, in Honour of Ask-Johannes and Michael-Roy 😊🎂😊🎂
The new ages tomorrow of Ask-Johannes and Michael-Roy will be numbers of the same parity (meaning both even or both odd, as mentioned earlier), and Ask-Johannes will still be a teenager. The product of the two new ages will be almost 222.
Part 1: What precisely are the two new ages if I tell you that their product is the largest number it could be that fits with the clues?
Part 2: How exactly do you know that the product cannot be 1 more than in Part 1? There might seem to be a solution which works with the larger product, but why doesn’t it?
Part 3: To determine the correct new ages in Part 1, why was it important to know that they are numbers of equal parity?
Part 4.1: Ask-Johannes’ older teenage sister, Vilja, had her birthday last week. Tomorrow, Ask-Johannes’ new age A will be of equal parity to Vilja’s age V. How old is Princess Vilja?
Part 4.2: What is most special about the day coming in A+V days from now?
Part 5: Scott Fleming from Arbroath, Scotland, is one of my friends on Facebook. I would like to offer early, advance, happy birthday wishes to Scott. A wee bonus puzzle for everyone else is to figure out Scott’s birthday (just the day and month) if I tell you that it’s in A days from now.
A Happy Birthday Brainteaser for Today, 21 November, in Honour of Murad, Marie, Ian and Chris, all friends of mine on Facebook!!!! 😊🎂😊🎂
The sum of the four friends’ new ages is 212, a palindrome.
Murad is the youngest, but finished being a teenager several years ago. He is now M years old.
The sum of Marie’s and Ian’s new ages is M+100.
Chris’s new age is the biggest of the four, and it’s a palindrome.
How old is Murad?
Quick, Wee Bonus Part 😊
A few days ago, I played in a Chess match in a very pleasant location at Hundelgemsesteenweg number 10*M in Merelbeke, Belgium. 👌
I won with Black in 10*M – 200 moves.
Everyone in the two teams was offered really nice complimentary refreshments during and after the Chess match.
Here are a few photos from the day.
It’s my intention to publish solutions to all the puzzles around the time that blog post #162 comes out, God-willing as always. (Before then, I will finally publish solutions to the puzzles of blog post #160 !) By the way, without needing to calculate the results, which of the numbers 158, 161 or 162 equals the product of two numbers of the same parity (given that one of the three choices is correct)!?
Please do feel free to send me your best solutions to any or all of the puzzles, if you like 😊.
I would like to round off this article by most sincerely wishing you a very blessed month of December soon, with lots of happiness in everything that you do ❤.
With kindest wishes as always,
Paul M😊twani ❤
“The Lord always forgives everything! Everything! But if you want to be forgiven, you must set out on the path of doing good. This is the gift!”–Pope Francis.
P.S. = Puzzle Solutions (being posted now on 27 December 2023)
The boy standing up must have won his Chess game. Reason: The total number of points for each game is 1 (either 1 point to the winner or 0.5 to each player in the case of a draw). So, the total for the two games involving four seated players was 2 points, but we were told that the grand total–including the boy visibly standing–was 3 points. Therefore, he scored 1 point, which means that he must have won his game. 👍
PRAY IT→PARITY
PREP HOW→WHOPPER
FED MORE→FREEDOM 😁
Ask-Johannes = 16 & Michael Roy = 30. 16 x 30 = 480, just four less than 484 = 222.
Note that 483 = 3 x 7 x 23, which doesn’t involve any teenage option.
The same is true of 482 = 2 x 241.
481 = 13 x 37 might seem to work, but we were basically told that Ask-Johannes was already a teenager, and so he wouldn’t just be turning 13 this year.
Also, being told that Ask-Johannes and Michael-Roy have ages of equal parity enabled us to be sure that the solution was 16 x 30 = 480 rather than 480 = 15 x 32 (which would involve numbers of different parity). 🙌
Princess Vilja = 18 (older than Ask-Johannes, but still a teenager whose age is of the same parity). 😊
A+V = 16 + 18 = 34, and 34 days after the first publication date of this blog post was…Christmas Day!! ❤️
Scott Fleming’s birthday was on 7 December. 🎂
Murad = 23 (Marie + Ian→123; Chris = 66; the grand total = 23 + 123 + 66 = 212). 👌
161 = 7 x 23, the product of two (odd) numbers of the same parity.
Note that neither 158 nor 162 are multiples of 4, and so neither of them could be the product of two even numbers. ✔️
Paul Motwani 