Here is one of the interesting things I learned while picking up Morse code. I can’t believe I have lived all my life without realizing this.

What does the term “SOS” stand for? Growing up, I always thought that it stood for “Save Our Souls”. I believe I first heard this while reading about the story of the Titanic. Some think of it as “Save Our Ship”.

It turns out that “SOS” is not an abbreviation at all. About 75 years after Morse code was created, around the start of the 1900s, the Germans helped set a universal distress code: SOS. They chose it because its Morse pattern [… — …] was easy to recognize. Before SOS, other distress signals were used, with “CQD” being the most common.

So, SOS does not stand for any English phrase. And even if it did stand for something, it would have been very likely a German phrase!

Did you know that?

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.

This is the Wordle problem from yesterday. I tried my usual first word. And hit jackpot with the second word. Got all the five letters but none of them were in the right position.

Then I got distracted. Instead of solving the Wordle problem, my idiotic brain converted it into a math problem. The question I had for myself was – in how many ways can I arrange the five letters (there is no repeat) where none of the letters will occupy the same position as the all yellow row. In other words, how many combinations of LATER can you come up with where the first letter is not L and second letter is not A and …. (you get the drift).

It is MUCH harder than I thought. One hour later, I realized I was getting late for office. Quickly solved the Wordle part and wrote to my nephew in UC Riverside before getting ready for work.

We still do not have an elegant solution. In desperation, I enumerated all possibilities. I have the answer now but do not know how to solve it.

HELP!!

Or at least, I found it to be difficult

Answer posted here