Dear Readers,
Happy New Year, 2021! Earlier today, I gave a brand-new brainteaser to my smart and lovely wife, Jenny. She said that it’s quite tricky, but she still succeeded in solving it within a few minutes! So, if you also like puzzles, then I warmly encourage you to enjoy tackling the fun brainteaser. In case the puzzle is not your ‘cup of tea’, I still most sincerely wish you a very happy New Year filled with love, joy and peace.
Wishing everyone a wonderful weekend now, too
Paul Motwani xxx
HAPPY NEW YEAR 2021 FUN BRAINTEASER
Ann and Bob are a married couple who have several children. Bob is older than Ann, but their birthdays are on exactly the same day of the same month. The funny thing is that, if we multiply their whole number ages together and add on the number of children they now have, the final result is a SQUARE number. That calculation will work this year and in EVERY future year for the same family: the result will always be a square number. In 2021, the result of the calculation is actually a year in the 21st century.
Question: What will be Ann’s and Bob’s respective ages on their birthday in 2021, and how many children do they have?
The solution will (God-willing, as always) be published at the time of the next blog post. In the meantime, staff members and lucky students at my school (Musica Mundi School in Waterloo, Belgium), or other students whom I work with personally, can win prizes if they send me a correct solution by email; otherwise Jenny gets all the chocolates!!
BRAINTEASER SOLUTION (being posted on 9 January 2021)
Warm congratulations to my wife, Jenny, and to Louise (a very clever student of mine) who both figured out that (in 2021)
Ann will be 43, Bob will turn 47, and they have 4 children.
It’s quite beautiful that 43 x 47=2021, and adding 4 gives 2025 which equals 45 squared.
Next year, (44 x 48) + 4=2116=46 squared, and so on…forever!
Paul Motwani 
I was given this puzzle by my chess-playing son Tim Mifsud. After solving it by trying out a few numbers I was pleased to get the mathematical theory behind it. ….it s actually a difference of two squares problem a sq -b sq =(a-b)(a+b). Then a sq = (a- b)(a+b) +b sq. The number of children is b sq ….so 4 or 9….I think we can rule out 16 children etc and the ages are in brackets . We can find a by the condition that the age squared will be a year in the twenty first century.
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Dear Mary,
Thank you for your very nice message!
You are totally right about the mathematical theory behind the puzzle.
The solution with 4 children is basically unique because of the key word ‘SEVERAL’ in the original statement of the puzzle.
If the word ‘SEVERAL’ had not been used, then alternatives with 1 child or 9 children could be attempted, but 9 is rather too great to fit ‘SEVERAL’ and 1 is too small, of course.
Thank you again most sincerely for your message, and I wish you and your family a lovely weekend now.
With kindest wishes,
Paul Motwani.
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The same to you and to your family. I admire your enthusiasm as a teacher and educator…I taught Physics for 42years but now am happily retired. Stay safe and regards from Malta.
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What a kind message! Thank you so much, Mary!
Wishing you a very good night now,
With sincere thanks again,
Paul.
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