Blog Post #95: For Two Lovely Ladies xx

Dear Readers,

This blog post is specially dedicated to the two lovely ladies pictured here.

There are numerous nice surprises prepared for the sweet sisters, and you can also enjoy following their treasure trail of goodies about to appear…!

The lady on our right, when facing the photo, is Annabel, the wonderful House Mother at Musica Mundi School (where I work as the Mathematics Teacher). We’re wishing her sister a fabulous, fun birthday today. She has a beautiful name that you’ll discover via a pair of puzzles!!

Feel free to grab a calculator first!

Puzzle #1

1. Start with any proper three-digit whole number that you like (e.g. 462)
2. Repeat it to get a six-digit number (e.g. 462462)
3. Multiply your six-digit number by 2, in honour of the two sisters
4. Now multiply by 3, my personal favourite number !
5. Divide by 13, the total number of letters in HAPPY BIRTHDAY
6. Finish by dividing by the three-digit number that you chose at the start.

Thanks and congratulations for (hopefully!) getting the result 462  !

4 x 6 x 2 = 48 for the beautiful birthday lady’s special day today.

Also, making double use of the first two digits from our 462,

it’s (4 + 6) x (6/4) = exactly 15 years to-the-day, today, since Annabel first arrived in Belgium.

Puzzle #2

Some of my students at the school (including Dante, Joshua, Kristina…) know that I love

AUROSONIC TRANCE

music!

Using our 462 again, and the letters in AUROSONIC TRANCE,

keep the first 4 letters; cross out the next 6 letters; keep the next 2 letters only,

and you find the beautiful name of AURORA.

Puzzle #3

Aurora’s son (and Annabel’s nephew), John Rick, has his birthday on exactly the same day and month as Annabel’s birthday. In honour of the young squire, start with the words

BE A KING

and remove just one of the seven letters, then (with the remaining six letters) make a proper six-letter English word which is something that Aurora loves!

The following magnificent cake was actually for Annabel’s 1-year-old grandson, Zyk, but it gives a nice clue towards confirming the answer of BAKING !

Puzzle #4

This 4th puzzle will take us back at least 4 years…!

1. Start with Aurora’s age before today, 47
2. Divide 2021 by 47
3. Note that the quotient, 43, was Aurora’s age (just counting whole numbers, from 26.2.2016 onwards) until the end of 25.2.2017
4. Now start afresh with the number 2017
5. Multiply 2017 by 13, the total number of letters in AURORA/ANNABEL or in HAPPY BIRTHDAY !
6. The result of 26221 is especially for Aurora, to again wish her a really fabulous, fun time on her birthday today, 26.2.21 !
7. It’s extra-nice that 2 x 6 x 2 x 2 x 1 = 48, for the birthday lady!

Puzzle #5 in this Blog Post #95 !

1. 48 squared = 48 x 48 = 2304
2. 47 squared = 47 x 47 = 2209
3. So, 48 squared – 47 squared = 2304 – 2209 = 95
4. It’s actually a mathematically-connected fact (not a coincidence!) that 47 + 48 = 95, too, but that’s because 47 & 48 are consecutive numbers
5. FUN CHALLENGE: I’m now thinking of the only other two positive whole numbers (other than 48 & 47, so let’s call the two new numbers x & y) for which x squared – y squared = 95. Can you discover exactly which numbers they are? (Note: This time, y & x are NOT consecutive numbers.)

That will be a prize puzzle for my personal students as well as for anyone at Musica Mundi School who might like to enjoy zapping and cracking it!!

A solution will (God-willing as always) be published at the time of the next blog post, or possibly even sooner.

’95 Puzzle’ Solution (being posted now on 27.2.2021)

An extremely useful mathematical fact to know is that x squared – y squared always equals (x + y) * (x – y). Now, 95 = 95 * 1 or 19 * 5. The first case leads to the solution given earlier, involving the numbers 48 & 47, since (48 + 47) * (48 – 47) = 95 * 1. The other solution is: (12 + 7) * (12 – 7) = 19 * 5 = 95.

So, x = 12 & y = 7.

Warm congratulations to Jane, an excellent student who cracked the puzzle.

I wish everyone a wonderful weekend now, and particularly happy celebrations for Aurora, Annabel and their whole family.

With kindest wishes as always,

Paul Motwani xxx