Many moons back, my friend Mita Basu had introduced me to this game – travle.earth. The whole idea is to travel from Country A to Country B by crossing only land borders. There are some quirks in the game – It thinks of Siachen Glacier as a country, it does not think you can cross from Morocco to Western Sahara by land, and for some reason, it will not let me go from Poland to Russia directly, although I have been to their land border myself (exclave of Kaliningrad).

But I have now reached the 1000 game mark without failing once. And I am ready to move on to my next geography game. First, I have to dig through my messages from Mita. About a month ago, she sent me another game that I haven’t opened yet!

If you want to learn about country boundaries, this is a great game to try.

Which of the following statements – if any – is/are true? How do you logically work it out?

1. Exactly one statement in this list is false.
2. Exactly two statements in this list are false.
3. Exactly three statements in this list are false.
4. Exactly four statements in this list are false.
5 Exactly five statements in this list are false.
6. Exactly six statements in this list are false.
7. Exactly seven statements in this list are false.
8. Exactly eight statements in this list are false.
9. Exactly nine statements in this list are false.
10. Exactly ten statements in this list are false.

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/

I thought it to be a fairly simple problem. Now I am stuck. I was reading a book that talked about organizational efficiency. It talked about 3 parameters. Each parameters can take the value of 1 thru 10. So, there are 1000 combinations.

It is at this point, I got totally distracted. The quick thought that came to me mind was how many different products can I get? And ever since, the book be darned, I cannot get my mind off it.

So, to repeat, there are three spots. You can fill each one of them with a number 1-10. So, you get 1000 possibilities. If you take the product of those 1000 possibilities, you will get 1000 numbers. But there will be repeats. For example,(1,2,3) (1,3,2) (2,3,1) (2,1,3) (3,2,1) (3,1,2) (1,1,6) (1,6,1) (6,1,1) will all give 6 as the product.

How many distinct products can you have?

Take 18 matchsticks and arrange them to form the number 508. I realized that we do not have matchsticks in our home and certainly, we do not have 18 gaslighters – so, resorted to powerpoint to make the picture.

Now, the question is by repositioning two sticks (any two sticks of your choice), what is the highest number you can get? Post your answer in the comments section.