Dear Readers,
Yesterday, I said to Max, “Have a wonderful, happy birthday in a week’s time!”, and tomorrow Max could say exactly the same to me!
Max, a great student at my previous school.
OK, so you already know that Max and I both have June birthdays, with Max’s on the 11th, and mine on the 13th. Let’s enjoy a wee dose of fun with those numbers and more…
Start with your favourite three-digit number (e.g. 116) and repeat it to get a six-digit number (e.g. 116116). Divide by 7, the total number of letters in PUZZLES. Now divide by 11, for Max’s birthday next Friday. Also divide by 13, for my birthday next Sunday. Hopefully you’re now smiling as you’re back with your favourite three-digit number 😊.
As Max likes drawing, let’s join him in accurately drawing a large square, and label the corners I, M, A, X. (Make the base side horizontal, for convenience.)
We’re now going to draw an isosceles triangle inside the IMAX square. The full base side of the square will also be the base side of our isosceles triangle, and its two base angles are to be equal.
I bet you know exactly where to put the third corner of the triangle in order to make its area as large as possible… Please take your well-deserved place at the very top 😊 in the centre of the square’s top side.
Connect up the three vertices (corners) to get a neat isosceles triangle. (Note: The green triangle image above couldn’t be our actual triangle because the top would be outside the square!)
Now, using a protractor OR a calculator, figure out (to the nearest degree) the size of either one of the triangle’s base angles.
Well done for getting 63° to the nearest degree. (Trigonometry fans may like to note that the exact size of either one of the base angles is tan-1(2), which is 63.4° correct to 1 decimal place.)
Let’s just take it as 63. If we now add on Max’s current age plus the new age he’ll be on Friday, we’ll get 90, like a perfect right angle!
Congratulations for figuring out that Max will be turning 14 (since 63+13+14=90).
Time for a quick joke…
Knock, knock.
Who’s there?
Max.
Max who?
Max no difference. Open the door!
Given that I should be turning 59 on the 13th, I hope that you’ll love the solution to the following fun brainteaser…
If HOLY + HOPE = LOVE
and different letters stand for different digits while same letters stand for same digits, can you discover the unique proper solution to the word sum puzzle when E is 3, my favourite number of all 😊!?
The solution will, God-willing as always, be published after readers have had some time to enjoy the challenge.
SOLUTIONS (being posted now on 30.6.2021)
If E=3, the unique solution then is 2950 + 2963 = 5913, which was quite beautiful for turning 59 on 13 June 😊!
In the meantime, let’s round off now with a beautiful chess study from 1970 by Alois Wotawa. It was highlighted recently on Facebook by IM Cyrus Lakdawala.
It’s White to play and win.
The chess solution will be published at the same time as the numbers brainteaser solution.
(Now on 30.6.2021) 1 Rc7!! threatens 2 Ba5# and intends 1…Kxc7 2 Bg3+ followed by Bxh2, or 1…a5 2 Bf2+! Ka6 3 Ra7# or 2…Kxc7 3 Bg3+.
Wishing everyone a wonderful weekend now,
Paul Motwani xxx
Paul Motwani 