Usually, it is her sharp wit and acerbic comebacks. And at times it is her math capabilities. (It does take a nerd to recognize another).

Recently, my nephews had sent me a puzzle. Using 1, 1 and 1, you have to make 6. Similarly, using 2, 2 and 2… and then 3,3, and 3… and so on. You can use the normal mathematical operators – but no other digits. For example 2+2+2 = 6; They had given me till 10,10,10.

8 is a little tricky. It would be 8 – sqrt (sqrt (8+8)). Note that sqrt symbol does not use a digit.

During the walk last evening, Niki and tried 11,11,11 and then 12,12,12 and so. Once we reached 19,19,19… she said something that helped us find a completely generic way of getting to 6 given any number (repeated thrice).

For example, can you get 6 using 73, 73 and 73?

Note that you cannot split 73 into 7 and 3.

The mathematical operators allowed (any number of times) are plus, minus, multiply, divide, parentheses, square root, log and factorial. Give it a shot!

I am getting a little worried that in all their puzzles, somebody or the other is getting killed (I think they are watching too much Bollywood) 🙂 , but the problems are interesting. I am attaching the Whatsapp screenshot here…

I sent this to my nephews since they have been sending me a few puzzles. See if you can beat them to it…

Orange circle inscribed inside an equilateral triangle inscribed inside a larger circle. Can you prove that the orange area is the same as the addition of the two purple areas?

Reeling under the lack of power, water supply and all that the devastating cyclone Amphan left behind, apparently my nephews hunkered down and started doing puzzles. They could not wait for power to come back – so that they could recharge their phones and send me this problem thru Whatsapp.

Good problem. About 2 years back, I had posted a similar version of the problem.

This week is another area problem. Take a rectangle ABCD (as shown here). Draw two lines from the adjacent vertices A and D to two random points E and F on the opposite side such that they intersect within the rectangle. See picture below. Nothing is drawn to scale. The area of the two triangles are 4 and 16. One of the quadrilaterals has an area of 10. What is the area of the other quadrilateral?

Again, this is geometry from elementary school with a twist to it.

Note that the original version of the problem that I had posted had the quadrilateral area as 1 instead of 10. Harmindar Matharu successfully proved that such a diagram is not possible. I should have been more careful while picking some values for those areas…