Dear All,
In the previous blog post, I featured ‘The Saints’ Little Book of Wisdom’, which is such a precious gem of a book that I am very warmly recommending it again here, to everyone. There are so many good things to learn by reflecting on and practising in our lives the pearls of wisdom contained in the book.
from St. Teresa of Avila is: “You pay God a compliment by asking great things of Him.” 💕
As usual, I also have several good-fun puzzles to share 👍😊
A Kettle Puzzle! 😊
My kettle at home displays 100 when the water in it boils. Afterwards, as the water cools gradually, the display number drops by 1 unit (degree Celsius) at a time, until it finally settles at around room temperature.
Looking at the photo above, I said to myself, “The temperature has dropped by 72° (from 100°) down to 28°. 72 x 28 = 2016.”
Kettle Puzzle Part 1
If I were to observe the temperature all the way while it dropped from 100°, and at each moment calculate
Temperature drop from 100 x Temperature displayed
what would be the maximum result that I could get like that? ✔️👏
Kettle Puzzle Part 2
The example result of 2016 (given above) ends with a 6. What is the probability that I could get a result ending in my favourite 3? 😍
(Please assume that I do my calculations correctly!!)
Cheers to Chess Puzzle!
Instead of drinking hot chocolate as in the photo above, I often drink delicious Musica Mundi School apple juice while I’m enjoying Chess with the students.
Suppose that 46 students drink a collective total of 350 cups of apple juice, and they all drink at least one cup each.
Cheers to Chess Puzzle, Part 1
As a very reasonable mental Maths exercise (without using any calculator), figure out, correct to 1 decimal place, the Mean (Average) number of cups of apple juice drunk per student.
Try to write a sentence or two to describe clearly the method you used to figure out your answer mentally. 👍
Cheers to Chess Puzzle, Part 2–A Brainteaser!! 😘
Given the information stated before Part 1, what is the maximum possible value for the Median number of cups drunk?
Cheers to Chess Puzzle, Part 3
If the maximum possible Median actually occurs, then what is the Modal number of cups drunk?
Also, what is then the Range = Maximum – Minimum number of cups drunk?
Welcome to Misato, Puzzle!
Misato, our newest wonderful student at Musica Mundi School, came all the way from Australia to Belgium this week. Helen, one of the English teachers, told me that Misato is really strong in her subject. So, I made now a nice word puzzle in honour of Misato.
Word Puzzle for Misato, Part 1
Remove just the letter A from MISATO, and then rearrange the remaining 5 letters to make a proper 5-letter English word. Try to find two different, correct solutions. ✔️👍
Word Puzzle for Misato, Part 2
Remove just the letter I from MISATO, and then rearrange the remaining 5 letters to make a proper 5-letter English word. Again, try to find two different, correct solutions. 👏
A Cute Double Checkmate Chess Puzzle!!
If it’s Black to move, checkmate can be forced in 5 moves.
If it’s White to move, checkmate can be forced in 4 moves.
Have fun solving that cute double checkmate Chess puzzle!! 😍
It’s my intention to publish solutions to all the puzzles around the time that blog post #161 comes out, God-willing as always. (Before then, I will finally publish solutions to the puzzles of blog post #159 !) By the way, without needing to calculate the result, which of the numbers 159, 160 or 161 equals the sum of the first eleven prime numbers (given that one of them is correct)!?
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 by most sincerely wishing you a very blessed month of November soon, with lots of happiness in everything that you do ❤.
With kindest wishes as always,
Paul M😊twani ❤
“In all created things, discern the providence and wisdom of God, and in all things give Him thanks”–St. Teresa of Avila.
P.S. = Puzzle Solutions (being posted now on 30 November 2023)
Kettle Puzzle Part 1: Maximum-possible result = 50 x 50 =2500.
Kettle Puzzle Part 2: None of the results in this particular Maths “story” can ever end with a digit 3, and so the probability of such a result occurring is simply zero. (Basically, it was a “trick question”!! 😁)
Cheers to Chess Puzzle, Part 1: To calculate 350 ÷ 46 mentally, one method is as follows…
7 x 46 = 7 x (50 – 4) = 350 – 28 = 322, with 28 still “to spare” from the 350 cups in the puzzle.
Next, 28 ÷ 46
= (23 + 5) ÷ 46
= (46/2) ÷ 46 + (4.6 + 0.4) ÷ 46
= 1/2 + 1/10 + nearly 1/100
= 0.5 + 0.1 + less than 0.01.
Putting that together with the chunky 7 found earlier…
the correct quotient result for 350 ÷ 46 will be…
7.6 for the Mean, correct to 1 decimal place ✔️
Cheers to Chess Puzzle, Part 2: Imagine the 46 students lined up in order, starting with the students who drank the least number of cups, and then going all the way up to the students who drank the most. The Median will be found in the middle of the long line by calculating
(the total number of cups drunk by Student #23 & Student #24) ÷ 2.
To maximise that result, let the first 22 students drink only 1 cup each (not zero, though, because we were told that everyone drank at least one cup each). Then, we have retained 328 cups to share amongst the final 24 students.
328 ÷ 24 = 13.7 (approx.), and so the most that we can allocate to Student #23 is 13 cups (whole number).
Then 315 cups still left ÷ 23 students = 13.7 cups per student (approx.), and so the most that we can allocate to Student #24 is again 13 cups (to also have a whole number of cups for him or her).
Therefore, the maximum-possible Median = (13 +13) ÷ 2 = 13 cups. 👌
Cheers to Chess Puzzle, Part 3: Following on directly from everything written in Part 2 above, imagine that we just give Students #25 up to #46 only 13 cups each. We’ll have “used up” 22 x 1 + 24 x 13 = 334 cups with just 16 cups still “to spare” from the total of 350.
At that moment, 22 students have 1 cup each & 24 students have 13 cups each (and we’ll get to the spare 16 in a wee moment!). As things stand right now, the mode is 13. It’s the “winner”!
Can any other number overtake it in popularity, by using the “spare” 16 cups…?
Well, if (for example) we bumped up 16 of the numbers 13 each to 14, then we’d have this situation: 22 students with 1 cup each, 8 students with 13 cups each, and 16 students with 14 cups each. The mode in that case would be 1.
To illustrate a couple of other alternatives…we could have 6 students with 1 cup each, 16 students with 2 cups each, and 24 students with 13 cups each. The mode in that case would be 13.
We might alternatively have 22 students with 1 cup each, 22 students with 13 cups each, and 2 students with a “lucky 21” cups each! The joint winners there for popularity are 1 and 13: they are both modes in this case, and in summary they are the only possible modes when the maximum median of 13 occurs. 👍
Word Puzzle for Misato, Part 1
MISATO – A = MOIST or OMITS.
Word Puzzle for Misato, Part 2
MISATO – I = ATOMS or MOATS or STOMA. 👏
A Cute Double Checkmate Chess Puzzle!!
If it’s Black to move, checkmate can be forced in 5 moves with 1…Rg1+! 2 Rxg1 Rxg1+ 3 Kxg1 Qg4+ 4 Kh1 (longer than 4 Rg2 Qxg2#) 4…Qd1+ 5 Rf1 Qxf1#.
If it’s White to move, checkmate can be forced in 4 moves with 1 Qa8+ Kd7 2 Qb7+ Kd8 3 Qb8+ Kd7 4 Qc7#. 😍
Regarding the sum of the first eleven prime numbers, 2+3+5+7+11+13+17+19+23+29+31=160. Even without calculating the actual result, we could know that it had to be even, because ten odd numbers make 5 pairs of odd numbers, equivalent to a sum of 5 even numbers. That has to be even, and adding on 2 (the smallest prime, and the only even prime) keeps the total even for sure. 😊
Paul Motwani 