Inside a right angled triangle with sides of 3,4 and 5 units, is inscribed a square with one side of the square on the hypotenuse as shown in the picture. The question is what is the area of the square?

I was driving back from the airport when I got a call from my old buddy SK and his son. Apparently, they were stuck on a math problem. What I understood is this:

SK’s son and his friend are trying to get two tickets to a concert. (He told me the name of the concert but of course, that was all Greek to me). The organizers are opening 50,000 slots you can apply to. And they will pick 4,500 of them as winners. In other words, there are only 4,500 seats available.

SK’s son and his friend bought 25 slots.

Question was what is the probability that the two friends would be able to go to the concert?

Apparently ChatGPT was saying 90%. SK’s intuition was far lower than that. His son felt that it made sense. So, over the phone we worked out the approach and agreed it will be a high number.

I got a message yesterday from SK that his son and his friend are indeed going to the show!

This early morning, curiosity got the better of me and I sat down with paper and pen to figure out what the probability would be.

Now, I am stumped! My answer is very different from what SK and his son reported as ChatGPT’s response was.

What do you think is the probability?

Answer published here

This puzzle comes from my good friend Amrith.

Fill the three vertices and two spots on each side of the triangle with the numbers 1 thru 9 (using each only once) such that each side adds up to 20.

Multiple solutions are possible.

What approach did you use (other than simple trial and error)?

Answer posted here: https://www.rajibroy.com/2025/08/22/answer-to-triangle-and-9-digits/