Dear Readers,
I have the pleasure of teaching Mathematics at Musica Mundi School (MMS) in Waterloo, Belgium. Today’s blog post is dedicated to Kate and Helen, two great colleagues whose birthdays are coming up very soon during the next school holiday break. The ladies collaborate excellently in their teaching of Global Perspectives, for example, and they are both very skilled in English language work, too, and so I think that they’ll enjoy the following anagram tribute in their honour. The 28 letters in FOR GREAT TEACHERS KATE AND HELEN rearrange perfectly to make AKA GREEN SECRET OF THE HEARTLAND 💚
‘Let my sentence come forth from Thy presence; let Thine eyes behold the things that are equal.’
I thank God with all my heart for giving all the ideas contained in fresh, brand-new prize brainteasers here, which are certainly among my absolute favourites from my life, so far.
💚A Fresh ‘1970s’ Brainteaser In Honour of Kate and Helen 💚
Imagine that the total number of pages in a beautiful, big Global Perspectives book is N, a three-digit whole number in which all three digits are positive and different from each other. By rearranging the order of the digits in N, Kate is able to form five new, different three-digit whole numbers. Helen adds up Kate’s five new numbers and correctly finds that the total sum is Y, a year in the 1970s. That is, Y is a whole number somewhere between 1970 up to not more than 1979.
Your special brainteaser is to figure out, with proof, the exact value of N and the exact value of Y.
Note that this is a very precise mathematical brainteaser. There is no random guesswork involved, and though calculators may be used, they are not strictly required.
Anyone who knows me well, knows that 3 is my absolute favourite number of all 😊😊😊! So, I’m more than happy to now celebrate one other upcoming MMS birthday, in addition to those of Kate and Helen! Next Friday will be the birthday of Lovely Lara, a Hungarian student at the school.
💚 A Fresh L-shape Brainteaser in Honour of Lovely Lara 💚
The image shows an inverted L-shape. Each line of the shape is either horizontal or vertical, just as you would expect from the appearance of the diagram. Assume that all the lengths of the lines are exact whole numbers of centimetres. However, note well that the diagram is certainly NOT drawn to scale!
Now, have a look at the horizontal line going across from the bottom of the side marked C. Imagine extending the left-end point of it with a dotted horizontal line to meet the side marked A. Also from the same left-end point, draw a dotted vertical line upwards to meet the side marked B. You may be wondering whether the wee shape that you’ve now formed in the top left area of the L-shape is a square… Well, yes, I’m declaring now that it is indeed a square!
You are now also told that the total area of the L-shape is L square centimetres, and the total outer perimeter is P centimetres (of course, don’t count any inner “dotted lines” described earlier as part of P; only count the outer perimeter of the L-shape).
Another super-important fact is: you are now given that L = P.
Your brainteaser in honour of Lovely Lara is to figure out, with proof, the exact value of L.
You are always very welcome to send me by email your answers to some or all of the goodies, if you would like to do so 👍💚😊
I will round off here with the beautiful Bible verse Matthew 17:2 ‘There He was transfigured before them. His face shone like the sun, and His clothes became as white as the light.’
Paul Motwani 