Dear Readers,
At least seven of my colleagues and students have their birthdays coming very soon, before Easter or just shortly afterwards.
The nice prize puzzles in this blog post are dedicated to Raphaël, Seinel, Wout, Louis, Romeo, Simon and Alisa, and of course I wish all readers a really blessed, happy Easter, soon❤️
Imagine that my Musica Mundi School (MMS) excellent Maths colleague, Jens, gives positive whole numbers (one each, in order of increasing size) to Raphaël, Seinel, Wout, Louis, Romeo, Simon and Alisa. Note well: Just two people receive exactly the same number as each other; everyone else gets different, distinct numbers.
The seven numbers given by Jens are special because their Mean, Median, Mode and Range are all exactly equal to seven 👌😊
The image below does NOT show the actual numbers given by Jens! However, it does provide quite a helpful reminder regarding the mathematical meanings of Mean, Median, Mode and Range 👍
Fun Puzzle
Part 1: The first part of this fun puzzle is for you to figure out the numbers that could have been given by Jens to Raphaël, Seinel, Wout, Louis, Romeo, Simon and Alisa.😊
Consider: What is the minimum possible number that could have been given to Raphaël?
Also, what is the maximum possible number that could have been given to Raphaël?
Part 2: Instead, now suppose that the Mean, Median, Mode and Range are all still equal to seven, but more than two people receive the same number as each other. Your fresh challenge is to figure out the numbers that could have been given this time to Raphaël, Seinel, Wout, Louis, Romeo, Simon and Alisa. Enjoy investigating the possibilities! 🙌
At the school, I recently shared an algebra brainteaser which involved solving equations of the type A + 2AB + B = N, where N is a positive whole number and A & B are integers. Jens worked on it with great passion, and succeeded in rearranging the equation to an equivalent form that I had in mind when sending the brainteaser: (2A+1)(2B+1)=2N+1. The brainteaser is then actually simplified and is reduced to finding factors (positive or negative ones) of 2N+1, and equating appropriate factor pairs to 2A+1 & 2B+1. Then you only have to solve straightforward linear equations to figure out the possible values for A & B.
Jens and his father, Eric, love a really good, meaty Maths brainteaser! 😍 So do some very keen students, including Wout, Raphaël and others!
Here comes a fresh, brand-new, original brainteaser…😁
BRAINTEASER 😊😊😊
Part 1
Jens, Wout and Raphaël go into a secret Maths chamber, where three positive numbers are lying on a table. They each take one of the numbers.
Raphaël multiplies his number by the sum of the other two numbers, and gets the correct result, namely 5.
Wout multiplies his number by the sum of the other two numbers, and also gets the correct result, namely 6.
Jens multiplies his number by the sum of the other two numbers, and of course gets the correct result, namely 7.
They announce their results of 5, 6 & 7 to Paul, and challenge Paul to figure out the exact product of (multiplying together) the three numbers that were lying on the table in the secret Maths chamber.
What answer should Paul get for that product?
Part 2
Jens, Wout and Raphaël go back into the secret Maths chamber, where they find three new, positive numbers on the table. They repeat the same type of calculations as they did the first time. Coincidentally, their three results end up being consecutive positive whole numbers again (though not necessarily 5, 6 & 7 this time).
They announce their results to Paul again, and again ask him to figure out the product of the three numbers that were on the table. Please assume that Paul is on good form, and he figures out the product correctly! 😊
What is the probability that Paul’s answer will be a whole number?
You are, as usual, very welcome to send me by email your answers to some or all of the goodies, if you would like to do so 👍💚😊
As always, I thank God with all my heart for giving me a wonderful family, very dear friends, colleagues & students, and for also giving all the beautiful puzzle ideas in their & His honour 💕
I will conclude this blog post with the following lovely Bible verse from John 17:4
“Lord, I have brought You glory on earth by completing the work You gave me to do.”
Paul Motwani 