Hello World

I don't have much experience in writing blogs so I will just start with a short description and then some puzzles.

Placement season has been going good for me. Although I am not much interested in joining a company but solving puzzles has been fun. You just have to go, solve some questions and get selected. One of the most striking thing you would notice is attitude of people towards puzzle solving. It has changed drastically since last two months. Usually, if I ask somebody a problem, I get comments like "Kya fart maar raha hai", "such a nerd" (for more click here). But suddenly, everybody seems to be doing puzzles and that too a lot.

So, I thought why not we all do it together. We may find multiple approaches to solve the same problem. Here, I will try posting puzzles of the tests taken by companies, practice questions for the future tests, solutions and some random puzzles and some difficult mathematic problems. If you have some good puzzles and want to share please send them to me. Feel free to comment about anything. Also post your solutions in the comments.

I will start off with some of the questions from yesterday's test. Have fun!

Puzzles from the Optiver test

1. Can you make 25 by using numbers 2,4,6,8 ( using each number exactly once) with the operations +,-,*,/

2. Suppose you and your friend are wearing a hat. I came and marked either 0 or 1 on both the hats. Both the numbers might be same or different. Now, you can see the number on your friend's hat but not your own. Similarly your friend can see number on your hat.

Now, I will ask both of you one question, "What is the number on your hat?". If at least one of you answer correctly then you are saved else I will kill both of you. What will you and your friend do?

Clarification: You and your friend can not communicate after the numbers are written. The only information available is the number on the other person's hat. You can decide the strategy beforehand.

General Case: What if there are n people and the hats are marked from numbers 0 to n-1 ?

Random Puzzle:

3. Consider a town with only one circular street. There are four companies of milk which want to set their business in the town. Density of population is uniform across the circle and every person goes to the nearest store to get the milk. Company A get to chose a location first, then B, then C and finally D. Each company want to have as much as business as possible. Each company knows that others also want the same.

What location should company B choose relative to A?

Clarification: If there are two gaps of equal size left for D, then D will chose at random either one of those. B has to chose according to the worst case scenario.

I will post the solutions tomorrow.