Dear All,

This action-packed article is specially dedicated to Mr. Eric Van Steerteghem, the father of Jens Van Steerteghem who is an excellent colleague of mine at Musica Mundi School π

For several weeks, I have been preparing nice, early surprises for Eric’s birthday coming soon, but due to a dramatic mathematical malfunction of my time machine, Eric got transported back to a year in the 16th century!!

Very fortunately for me, and for Eric, I received invaluable help from the Mathematical Murphy Family in Operation ‘REVS’: Rescue Eric Van Steerteghem!

**REVS Challenges**!

- When a time portal opens, you have to expect the unexpected and be ready to act really fast! So, we had to make use of Samba’s great speed, and if possible try to stretch
…and Samba did it! In fact, the top speed she reached was an exact whole number in km/h and also in metres per second. What a quick and mathematical dog, she is!**slightly beyond**the official 50 km/h limit

**Using the clues above, figure out Samba’s exact top speed** π

2. If you look back to the lovely photo (earlier on) of the Mathematical Murphy Family, Benjamin’s pose is nicely representative of the whole family saying, “We’re ready!”

CΓ©cile’s favourite one-digit whole number–let’s call it C–also played a role and brought optimism to the rescue team in this way: If we start with 4808 (the elevation of Mont Blanc in metres), then replace the digit zero with C to get a new four-digit larger number, and then divide that larger number by C, amazingly…the result is the number 1212 from Eric’s photo (given earlier on)!

**Using the clues above, figure out CΓ©cile’s favourite number, C** π

3. An audio file retrieved from the time machine has revealed that, at the point of malfunctioning, the machine gave itself an instruction…

“REVERSE THE – – – – – – – – FIELD.”

**Try to figure out the missing 8-letter word**, given the extra clue that

REVERSE THE – – – – – – – – is an anagram of ERIC VAN STEERTEGHEM ! π

4. In case you’re wondering about which year Eric was born in, just *think of the high score that RaphaΓ«l got in a 100-mark test, multiply by the small number of marks that he lost, and double the result…*

**…to know the exact year when Eric was born! Have you got it?!** π

5. Florence’s favourite number–let’s call it F–is super-special!

As it’s a *three-digit whole number* with no repeated digits, we could write that

F = *top* with *distinct digits t, o and p*.

It has the property that

*tops multiplied by s = spot*

where s is also a different digit!

**Using the clues above, figure out Florence’s favourite number, F** π

6. If you’ve already figured out Florence’s favourite number F, then you’ll discover easily that F = H x H x HI, where H is a one-digit prime number and HI is a two-digit number with prime digits H & I.

*The loveliest detail is that calculating H x HI x HHI gives…*

** …Eric’s exact date of birth in the form ddmyy** (day number followed by month number and last two digits of his year)!!

**Have you cracked it?!** ππβ₯ππ

**TRICK** **BπNUS**: How many whole numbers exist for which the ** product** of the digits of such a number equals the new age that Eric will be on his birthday, soon!?

7. In the Mathematical Murphy Family, their favourite numbers are all whole numbers greater than 1.

If you were given the ** product, P, of** Christiaan’s and RaphaΓ«l’s favourite one-digit numbers, you’d find that P

*is a number which has precisely three factors*.

We haven’t yet come back to Albane Murphy, or mentioned Albane’s favourite one-digit number, A.

The giant breakthrough that really capped the rescue team’s success in Operation REVS was that ** C x A x P gave us the exact year in the 16th century to which Eric had been sent by the malfunctioning time machine**! (Reminder: C was CΓ©cile’s favourite number from earlier on.)

** If you can discover the exact value of C x A x P**, then please consider yourself a star rescuer, too!! πβ₯π

8. Now, you may well be wondering what made the confused time machine send Eric back to the specific year *C x A x P*…

…and the rescue team found the answer! When we figured out the **total giant sum, G, of all the proper divisors (or factors) of that year** (including the number 1, but not counting the year itself), the reason for the machine’s confusion suddenly became clear!

**Have fun calculating G **too! πβ₯π

By the way, that C x A x P year is the only year since the birth of Jesus for which the total sum of all its proper divisors = G.

It’s a unique year that we’ll no-doubt all remember for a looooooooooong time!

9. The day number of Eric’s birthday could be discovered in REVS Challenge #6, earlier on.

**Multiply the long number 12345679** (from which Samba already ate 8 as a wee snack!) **by Eric’s day number to get an even longer, special result here in Blog Post #148** πβ₯π

10. If a number, *pal*, and its reverse, *lap*, are both proper three-digit whole numbers, what is the largest-possible still ** three-digit** result for

**?**

*pal + lap*

11. What is the smallest-possible positive whole number E (in honour of Eric’s full 18-letter name, Eric Van Steerteghem!) which is a multiple of 148 and ends with the digits 148 on the right, and has 148 as the total sum of all of its digits? πβ₯π

**EXTRA BπNUS**: As it’s 28 January today, what is the smallest positive multiple of 28 for which the total sum of all its digits is 28 ? That can be solved very neatly using some nice logic πβ₯π

12. Change *one* letter B in EVS BIBLE to an E, and then rearrange to make one of my favourite 8-letter English words β₯β₯β₯

13. If you were to rescue me and then offer me a bowl of rice, I would say, “Yeees, please!” so quickly!

As there’s a total of 13 letters in Happy Birthday, we’ll have an extra-special, super-fun REVS Challenge #13 for Eric to enjoy π

Remember the number 1212 from the nice photo of Eric (earlier on)…well, I’ve got an equation for Eric which has exactly 121 solutions of 2 different types!

**SO x ERIC = RICE + YEEES** πβ₯π

Different letters stand for different digits and same letters stand for same digits.

If we allow the letter O to be zero, then we can get 120 similar solutions in which SO and YEEES don’t vary, but ERIC and RICE can.

If we don’t allow any zeros at all, then there is just one, unique solution to

**SO x ERIC = RICE + YEEES** πβ₯π

Jokes/Clues: Samba’s top speed in km/h is involved because it was * so* fast! Also,

*do I ask you to think about the number of*

**Y****distinct**letters in Benjamin!?

I wish Eric and his family, and all readers, lots of fun with the feast of puzzles in early celebration of Eric’s birthday β₯β₯β₯

It’s my intention to publish solutions to all the puzzles around the time that blog post #149 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 prepare to round off this article now by most sincerely wishing you a very blessed weekend, with lots of happiness in everything that you do β₯

With kindest wishes as always,

Paul Mπtwani β₯

“If the Lord is pleased with us, He will lead us into that land, a land flowing with milk and honey, and will give it to us.”–Bible verse, Numbers 14:8 β₯

Enjoy a wonderful movie-clip and a beautiful piece of Vangelis music known as * ‘Eric’s Theme’* via this link:

**https://www.youtube.com/watch?v=uwyltmUR3MU** β₯β₯β₯

**EARLY BIRTHDAY BπNUS CHESS PUZZLE FπR ERIC! π**

**P.S. = Puzzle Solutions** (being posted on 4 February 2023)

- Samba’s top speed was
**54 km/h, equivalent to 15 metres per second**. - CΓ©cile’s favourite number,
**C = 4**, because 4848 Γ· 4 = 1212. - ERIC VAN STEERTEGHEM β REVERSE THE
**MAGNETIC**! - 89 x (100 – 89) x 2 =
**1958**, Eric’s birth year. (Note that there were no other reasonable ‘solutions’, since 88 x (100 – 88) x 2 = 2112 & 90 x (100 – 90) x 2 = 1800.) - 1089 x 9 = 9801; Florence’s favourite number,
**F = 108**. - 108 = 2 x 2 x 27 &
**2 x 27 x 227 gives 12258 in honour of**. Trick Bonus: Eric will soon be 65, but there are*Eric’s date of birth, 12.2.58*because the prime factorisation of 65 = 5 x 13, and we can’t have a digit 13 !*no whole numbers with digits product equal to 65* - Given that P has precisely three factors,
*P must be the square of a prime number*. We already know that C = 4, and A is also a one-digit whole number. Consequently,.*the only suitable possibility for C x A x P that gives a year in the 16th century is 4 x 8 x 49 = 1568* - The
**proper**divisors of 1568 (including 1, but not 1568 itself) are**1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784**.**Their sum is 2023****π**Bonus: ERIC SPLASH – S =**SPHERICAL**. - 12345679 x 12 =
**148148148****π** - For
*pal + lap*, if the result is to still be a*three-digit*whole number, then the largest-possible option is 148 + 841 =**989**. - The smallest-possible positive whole number E (in honour of Eric’s full 18-letter name, Eric Van Steerteghem!) which is a multiple of 148 and ends with the digits 148 on the right, and has 148 as the total sum of all of its digits is the 18-digit number
. Extra Bonus: The smallest positive multiple of 28 for which the total sum of all its digits is 28 is:*999999999999999148***7588**. No three-digit number could be sufficient because the sum of its digits couldn’t exceed 9 + 9 + 9 = 27. Also, multiples of 28 are guaranteed to be multiples of 4, and so the last two digits (on the right) have to form a multiple of 4. Therefore, we can’t end with 99 or 98; instead, 88 is the best we can get. 28 – (8 + 8) = 12. So, we seek solutions for which the leading two digits (on the left) have a sum of 12.; it’s equal to 28 x 271.*7588 is the smallest number that meets all the requirements of the puzzle* - EVS BIBLE – B + E β
**BELIEVES**. - The following image shows the 121 solutions of 2 types to the equation that was created specially for Eric
**π**β₯**π**

**Quadruple Bonus Birthday Brainteaser**

Part 1: (JENS x ERIC) Γ· (NICK) simplifies to (JEERS) **Γ·** K, and that can be **minimised** with (2 x 1 x 1 x 4 x 3) **Γ·** 8 β**3, the smallest-possible integer result**. The values used for J & S are interchangeable, but R should be 4 as shown in order to keep ‘ERIC’ as high as possible for Part 2!

Part 2: ERIC should be 1 x 4 x 7 x 9β**252**. There, I = 7 & C = 9 or vice-versa, but 8 was not available because K = 8 from Part 1.

Part 3: JENS should be 2 x 1 x 6 x 3β**36** and NICK should be 6 x 7 x 9 x 8β**3024**.

Part 4: **The digit 5 was not used at all for any of the letter-values in JENS, ERIC or NICK**.

B**π**nus Word Puzzle: ERIC GET MOβ**GEOMETRIC** **π**

In the early birthday bonus chess puzzle for Eric, **Black should play 1…Kf7!, after which White is defenceless against the simultaneous threats of 2…Rh3# and 2…Nf8+ 3 Kh8 Rg8#**.