When this day (19 December 2022) began, there were exactly six days = 144 hours until the start of Christmas Day ♥
By midday at the centre or heart of each new day, God has granted us another 144 super-precious 5-minute gifts of time (as 144 x 5→720 minutes = 12 hours), and it’s good to aim to use all of them to thank and honour Him in everything that we do ♥
I found today that ABCDF contains more than one interesting idea. Thinking of the product of the numbers that correspond to the normal positions of the letters, 1 x 2 x 3 x 4 x 6 = 144, right here in Blog Post #144. I count myself and everybody as being the missing ‘E’ for ‘EVERYONE’… I know that we will all go on to G, H, I, J, K, L…with God in Heaven provided that we believe gratefully In Jesus, King of Love ♥
We could note very briefly in passing that L→12, the (square) root of 144, but it’s really much more important to recognise properly that God’s Love for all of us is at the root of our salvation.
As many of my students–and my colleagues–like puzzles, I’ll offer several now for everyone’s enjoyment 😊
Rearrange the letters of NEAR GIANT to make the name of a 9-letter country.
Rearrange the letters of MR TALENTS IN U to make a proper 11-letter word that all the students of Musica Mundi School use 😊♥😊
Special Puzzle in honour of my colleague Jens Van Steerteghem
JENS is a brilliant physicist, chemist & mathematician, too. Suppose that J=10, E=5, N=14 & S=19. Now here comes a super-fun puzzle…Add up the values of any two or any three of the four letters, then multiply by the left-over total, and divide by 4 in honour of JENS.
What is the maximum possible final result?
It’s a delightful wee Christmas present to Jens and everyone who loves mathematical puzzles, and in fact it’s possible to figure out the answer mentally using nice logic 😊♥😊
Puzzle Regarding A Lovely Lady (use A=1, B=2,…,Z=26 in this puzzle)
A former colleague of mine from my previous school in Belgium sent me a lovely Christmas card by email. In the lady’s six-letter first name, there’s no A. The product of the values of a certain four of the letters is 100. The product of the values of a certain five of the letters equals 5 x 144.
What is the exact product of all six letters? 😊
B😊NUS: Can you make a smart conjecture to guess the lady’s well-known first name, that many ladies have had?
A Really Beautiful Brainteaser ♥😊♥ (use A=1, B=2,…,Z=26 in this brainteaser)
Raphaël writes a proper six-letter English word that uses 5 distinct letters, including an R. The product of the values of all the letters in the word uses 4 distinct digits and begins with 5703…
Your mega-fun brainteaser is to figure out Raphaël’s six-letter word 😊
Chess Game in honour of my colleague Emile Daems
Emile Daems–a great colleague of mine at Musica Mundi School in Waterloo, Belgium–has been enjoying discussing some famous Chess openings with me. So, I’m including a photo of a recent game for Emile and other fans of The Royal Game ♥
A Whisky Puzzle in honour of my friends ‘Happy’ & Mandi!! 😊😊
Many people from Scotland and elsewhere enjoy some whisky! The word ‘whisky’ also brings ‘malt’ to mind, or the adjective ‘malty’. Here’s one description that I came across: “Generally speaking, a malt taste can be described as having a combination of flavours. It tastes sweet and nutty, but is also described as tasting similar to toast, caramel, coffee or fruits like raisins. The reason for its sweet, almost dessert-like taste has to do with how malt is made from barley.”
Here’s the puzzle now: Use all the letters of MALTY + H to make the name of a six-letter town where my friends ‘Happy’ & Mandi live, in the English county of Lancashire 😊
A Maths Mega-Brainteaser is coming next, in honour of my students and my brilliant colleague Jens & his ingenious brother Nick Van Steerteghem (who wrote a computer program specifically to solve another recent brainteaser!–special congratulations also to Raphaël Murphy who solved the brainteaser directly himself!!)
Imagine that I put the numbers 1, 2, 3, 4, 5, 6 & 7 (one of each) in a bag.
Raphaël, Tarik and Wout each take a number out of the bag.
Damla, Sophie and Jens also each take a number out of the bag.
I then announce, “The total sum of Raphaël’s, Tarik’s and Wout’s numbers is exactly equal to the total sum of Damla’s, Sophie’s and Jens’ numbers! Furthermore, the total sum of the squares of Raphaël’s, Tarik’s and Wout’s numbers is exactly equal to the total sum of the squares of Damla’s, Sophie’s and Jens’ numbers!!”
Your fun brainteaser is to figure out exactly which number is still in the bag.
Part 2 (Super-Tricky!!)
A large group of Maths fans goes with me to visit an old Spiritual Maths monk at a monastery on a high hill. The number on the monastery building is a proper three-digit number. When we get to the door and see the number, I tell everyone that the sum of the squares of its digits equals the monk’s age!
The monk’s age is also equal to the sum of the fourth powers of three distinct positive whole numbers (just meaning different from each other).
Your mega-challenge brainteaser is in three parts:-
2.1: How old is the monk?
2.2: What is the smallest possible three-digit number that could be on the monastery building, given the clues above?
2.3: What are the fourteen different possible three-digit numbers that could be on the monastery building, consistent with the clues? (Note: That’s fourteen answers including the answer to part 2.2.)
Note also that the Spiritual Maths monk is not hundreds of years old like Yoda!! The monk is at an age that many other people have reached, too, in human history. Of course, I didn’t strictly need to mention that. Even if the monk’s current age could have been, say, 144–or 22 years more than the oldest person on record to-date 😊!!–the first clue relating his age to the sum of the squares of the digits on the three-digit door number meant that he couldn’t be more than 9 squared + 9 squared + 9 squared, or 243 years old now!! Still, my sincere answer to the question, “What could be better than living to be 144+99 years old?” is: “Living forever in Heaven.”
It is my intention to publish full solutions (God-willing, as always) to Blog Posts #142 & 144 before 9 January 2023, when the next semester’s lessons at Musica Mundi School begin.
In the meantime, dear students, colleagues and other readers, please do feel free to send in your best solutions to any or all of the puzzles, if you like ♥
The school’s cats visit the Maths classroom frequently, and they’re already pondering the fresh puzzles now!! 😊😊😊
My family and I would like to wish you and everyone a very blessed, merry Christmas soon, followed by a wonderful, happy New Year ♥♥♥
With kindest wishes as always,
Paul M😊twani ♥
Meanwhile, here’s wishing Headmaster Herman a very happy birthday tomorrow!
Certainly let any nice school cat add the missing ‘E’ (from much earlier in the article), because SCHOOL CAT + E = CHOCOLATES
…and add comes from 144 😊
P.S. = Puzzle Solutions (being posted on 31.12.2022)
NEAR GIANT = ARGENTINA
MR TALENTS IN U = INSTRUMENTAL
Using the numbers on Cleo’s sweater, (6×6)(1+3) = 36 x 4 = 144
In the puzzle about JENS, since J=10, E=5, N=14 & S=19 have a total sum of 48, we can achieve the optimal result with (10+14)(5+19)÷4 = 24 x 24÷4 = 144 again! 😊😊
In the puzzle about the lady’s six-letter name, the product of all her letter values = 3600, the LCM of 720 (= 5 x 144) & 100
Her name is DEBBIE (with 4 x 5 x 2 x 2 x 9 x 5 = 3600) 😊
Raphaël’s six-letter word is MEMORY, for which the product of the letter values is 13 x 5 x 13 x 15 x 18 x 25 = 5703750
(There were some cases to check, but since we were given that the word included an R–with letter value 18–the overall product had to be an even number and also a multiple of 9, and so in this particular puzzle the last digit had to be 0 & the sum of all the digits had to be a multiple of 9, which helped enormously to narrow down the cases for checking 😊)
MALTY + H = LYTHAM, where ‘Happy’ & Mandi live 😊😊
In part 1 of the Maths Mega-Brainteaser, 2+3+7=1+5+6 and, crucially, 2 squared + 3 squared + 7 squared = 1 squared + 5 squared + 6 squared; the unused number 4 is left in the bag 😊
In part 2, we don’t have to consider 4 to the power of 4 because that’s 256, which is a bit too old!! Instead, 1 to the power of 4 + 2 to the power of 4 + 3 to the power of 4 = 1 + 16 + 81 = 98, the monk’s true age ♥
Now we know that 98 = the sum of the squares of the digits of the monastery’s three-digit door number, which could be any of:-
149, 194, 358, 385, 419, 491, 538, 583, 707, 770, 835, 853, 914, 941
since 1 squared + 4 squared + 9 squared = 3 squared + 5 squared + 8 squared = 7 squared + 0 squared + 7 squared = 98 in those cases or permutations of them; clearly 149 would be the smallest possible proper three-digit door number meeting the monk’s requirements! 😊