Blog Post #149: A Funny Tale of Pairs of Pairs of Furry Tails!! 😊♥😊♥

Dear All,

Mr. Jan Vanderwegen, an excellent colleague, IT expert and friend of mine at Musica Mundi School, enjoys being creative and thinking ‘out of the box’, just like his very clever trio of mathematical cats! 😊♥😊

Cute Coco likes square-based boxes…so we’ll certainly feature some sneaky puzzles about ***squares***! 😊

There on the comfy sofa, Coco, Marron and Noisette are dreaming up some fun puzzles in early celebration for Jan turning N*(N+1)*(N+2) years old next month, on day number (N+2)*(N+2) + (N+4)*(N+4) of this year 2023 😊♥😊

COOL CATS CHALLENGES!

How old will Jan be on his birthday next month?
What was Jan’s exact date of birth?
Remove just one letter from the word FEELING and rearrange the remaining letters to make a proper, six-letter English word.
Imagine me visiting the cats’ home as a – – – – -. Change the last letter of – – – – – to the letter immediately before it in the English alphabet. Can you guess what word you’ll have then?

MR. M😊’s FUN BRAINTEASERS

5. What is the smallest positive whole number for which its square begins with the digits 222?

6. What is the smallest positive whole number (with more than one digit) which becomes a square number if its reverse is either added to or subtracted from it?

The next brainteaser is going to feature Jan’s three cats…and one of my own…
so that we can have a funny tale of pairs of pairs of furry tails!! 😊♥😊♥

Imagine that I write down the ages (which are all different whole numbers of years) of Jan’s three cats and of my cat. **The range (or age difference) between the oldest cat and the youngest of the four is exactly double Jan’s favourite number**.

For **each** possible **pair** of cats among the four, I write down the sum of the two cats’ ages, until the list of sums is complete. Next, for **each** possible **pair** of sums from that list, I calculate the sum of the two sums involved! I put the results of those particular calculations in a box. The smallest result in the box is 22, and the largest result in the box is 50.
**Your fun brainteaser is to figure out Jan’s favourite number** ! 😊😊

By the way, where does a cat go if it loses its tail…?!

…It goes to the retail store!!

Did you hear about the secret agent Maths teacher who couldn’t get on the plane?!…
…He let the cat out of the bag!! 😊😊

Bright B😊nus: Suppose that the traditional colours of a rainbow, represented by ROY G BIV, correspond to the numbers 1, 2, 3, 4, 5, 6, 7 respectively. The product of the values of Jan’s two favourite colours is a square number.

What are Jan’s two favourite colours?

8. Jan’s second-favourite and third-favourite numbers are both odd whole numbers, greater than 1. One of them is larger than Jan’s favourite number which you (hopefully) found already.

With that given information, what is the smallest-possible product if we multiply Jan’s three favourite numbers together? (The true product may be higher, of course, but that can’t be confirmed without further information.)

9. The following neat chess puzzle is dedicated to Jan, and to James Gallagher–a former student of mine who is fascinated by ‘The Royal Game’.

**Black is threatening …Bh4#, but…it’s White to play and force checkmate in just 3 moves!** 😊

10. The Cats’ Sky-High B😊nus Birthday Brainteaser for Eric Van Steerteghem next Sunday!

As Eric’s birthday is coming in 7 days from now, on 12 February, Jan’s clever trio of cats have a sky-high bonus brainteaser involving a triangle and the number 84 = 7 x 12 for Eric 😊

Imagine a right-angled triangle in which the three side lengths (in centimetres) are each exact whole numbers. One of them is 84 cm.

Part 1 of the brainteaser is to figure out the maximum-possible perimeter of the triangle, and also its maximum-possible area.

Part 2 of the brainteaser is to figure out the minimum-possible perimeter of the triangle, and also its minimum-possible area.

It’s my intention to publish solutions to all the puzzles around the time that blog post #150 comes out, God-willing as always.

In the meantime, 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 now by most sincerely wishing you a very blessed Sunday, with lots of happiness in everything that you do ♥

With kindest wishes as always,

Paul M😊twani ♥

“You have already been pruned and purified by the message I have given you.”–Bible verse, John 15:3 ♥

Here’s Wishing You a Happy Valentine’s Day in 3 x 3 days from now…😊♥😊

P.S. = Puzzle Solutions (being posted on 17.2.2023)

Jan will be 3 x 4 x 5 = 60 years old on his birthday next month.
Jan’s date of birth was 15.3.1963. Note that 15 March is day number 74 or (5 x 5) + (7 x 7), in non-leap years.
FEELING – G →FELINE.
GUEST – T + S →GUESS.
149 squared = 22201.
65 + 56 = 121 = 11 squared & 65 – 56 = 9 = 3 squared.
Jan’s favourite number is 7. Jan’s favourite colours are Red and Green.
3 x 7 x 9 = 189.
In the Chess puzzle, White forces checkmate with 1 Rh5+! Kxh5 2 Qh7+ Kg5 3 h4#.
Part 1: The maximum possible perimeter is 84 + 1763 + 1765 = 3612 cm; the maximum possible area is 84 x 1763 ÷ 2 = 74046 square centimetres; Part 2: The minimum possible perimeter is 84 + 13 + 85 = 182 cm; the minimum possible area is 84 x 13 ÷ 2 = 546 square centimetres.