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! πβ₯π

**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. Mπ’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?

7.

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

*…It goes to the retail store!!*

Bright Bπnus: 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’.

10. *The Cats’ Sky-High* *B*π*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 π

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 π.

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 β₯

With kindest wishes as always,

Paul Mπtwani β₯

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

**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 β
**FELINE**. - GUEST – T + S β
**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 Γ· 2 =**74046 square centimetres**; Part 2: The**minimum possible perimeter**is 84 + 13 + 85 =**182 cm**; the**minimum possible area**is 84 x 13 Γ· 2 =**546 square centimetres**.