Three in a row

Hello LLs,
I today have come up with three interesting puzzles which are not as tough as they are expected to be. And probably, this is the reason that I am giving you three puzzles to solve. What you are supposed to do is solve three puzzles at a stretch, in as less time as possible. On the basis of survey I did with my fellow mates and friends, an average person will require five and a half minutes to solve all the puzzles together. One of the persons solved all three puzzles in just two minutes and twenty seconds. I hope you all can cross these puzzles in as less time as possible. All the best.

Puzzle #1:

There are three friends Sachin, Rahul and Saurav, who are talking about Anil. They all had been to painting exhibition and these are the statements they made.
Sachin: Anil has bought at least four Paintings.
Rahul: Anil has bought less than four Paintings.
Saurav: Anil has bought at least one Painting.

Only one of them is speaking truth.

Now, you have to guess the number of paintings Anil has bought.

Puzzle #2:

In my bedroom there are 20 black, 20 white, 30 red and 15 blue socks available. I went inside my room and it is all dark and no electricity available. Now, I need to have two pairs of Socks for my road trip. All socks of same colour are exactly same. 

You have to tell me that in all how many socks should I take outside my room that I will surely have two pairs of Socks. These two pairs can be of the same colour or the different colour. But in the same pair, socks have to be of same colour.

Puzzle #3:

Ravi and Sunil were sitting on the bank of the river. Ravi takes certain number of stones and hides in his pocket. Ravi then tells Sunil that he has certain stones, total number is either 1 or 2 or 3.

Sunil has to ask one question and determine the number of stones. He can ask the question and Ravi will answer in Yes, No or Don't know. What will that question be?

Enjoy. And don't forget to note the time. Signing off!

Spooky Number

As, we are following the trails of the numbers, we come to know strange things about them. But, believe me, no thing is as strange as this characteristic is.

What, you have to do is,
1. Take any four digit number. (Leading zero is permitted. But, all four digits can't be same.)
2. Arrange the digits in the number in the descending order. Consider this new number as M.
3. Arrange the digits in the number in the ascending order. Consider this new number as N.
4. Subtract N from M.
5. Go to Step 2 and repeat this procedure with the answer you got from subtraction.

You may take any number whatsoever. But, with certain series of repeating this procedure, you will always end up with one number. Which will then, keep repeating itself.

Isn't it spooky?
You take any number and still you will end up with the same number after certain operations. This number is known as Kaprekar's constant. And the above procedure is called Kaprekar's routine.

You, after taking a single number and repeating the procedure for n number of times, you will get to the answer. But, in this puzzle, it is not about getting the answer. It is about learning the strange characteristic.

This Kaprekar's constant has been given name from an Indian Mathematician Dr. D.R. Kaprekar. He has given Kaprekar, Harshad and Self Numbers. You can learn more about the mathematician and various numbers he came up with, with the help of Internet. All the best to you. Research More and More. And, if you have any idea about such strange numbers, come up with those.

Numbers speak more than words

Today, I am here to bring your attention to some extraordinary numbers , which look just like other numbers but carry some special attributes. And, as always, I won't bring you the solutions , you have to identify these numbers :

1, Armstrong Number:
There are some three digit numbers, which possess this characteristic. Armstrong numbers are those numbers, which equal to the sum of cubes of all its digits. There are four numbers having this characteristic. I will give you one. Find the other three.
153- here cube of 1…5…3 is 1…125…27 and sum of 1,125,27 is 153 itself. So, this number is called Armstrong number. Bring me other three. :)

2. Ramanujan Number:
First number which can be written as sum of two cubes in two different way.
You don't need much information in this criteria. Just test your brain and come up with the answer.

3. Perfect Number:
A number is called perfect, if sum of all its positive divisors excluding itself equal to that number itself. For example: 6
6 has positive divisors- 1,2,3 (and 6, which is excluded) so, its sum is 6 too. (1+2+3) Thus, 6 is perfect number.
(FUN FACT: THIS IS SO CALLED REASON WHY 6 HAS BIGGER INFLUENCE IN HISTORY.)
Get me other perfect numbers.

All the best Logic Lovers. I hope you will succeed. 

8 Queens' Problem

Hello Logic Lovers,
Today I am back with a very interesting and well known puzzle of N Queens' Problem. This puzzle is based on the game of Chess.
If, you hadn't come across Chess ever before, take a look at the chess board. I will brief you with the details that you need to focus during solving the puzzle.



Here, YOU ARE SUPPOSED TO PUT EIGHT QUEENS IN A WAY THAT NO QUEEN CAN KILL ANY OTHER ONE. 

Now, In what all ways a queen can kill...
A queen can kill any other queen if it is in the same row or column. And, in the same diagonal.

Now, for naming conventions of each square, we use combination of row and column number.

So, here, if one queen is on A8, you can't put other queen in row 8 and column A. In addition, the diagonal containing squares like: B7, C6, D5,..., H1 too can't contain another queen.

This is what the situation is and you have to come up with the solution of putting all eight queens. This is a known puzzle but an amazing brain twister.
If I can say, it is quite an easy one. As, there are total 92 solutions possible for this Problem. I am sure that you will be able to come up with at least one solution. All the best. For any further queries, you may comment here.

Who will succeed in Prison Break

Hello all. I am back with the new puzzle. Here, the scenario is of the prison. In which, prisoners were planning to break the jail. Now, the thing is that, there are switches available for the rooms in which they are staying. Here, the switch ON means that the gate is open and the switch OFF means that the gate is closed. But, there is no indicator that the switch right now is ON or OFF. Now, every prisoner is given a chance to go to the switch and open the gate of the room in which he is staying.
As, they were planning the break and no one in prison trusts anyone else. So, they wanted to come up with a solution through which they can be sure that no one will cheat and some of them will be able to break the prison. So, they decide that, every prisoner, when goes to the switch room will change the status of the switch of all the rooms whose numbers are multiple of the room number in which he is staying. ie, A prisoner in room no. 2 will change the status of switch of all rooms having numbers: 2,4,6,8....
Now, there are total 1000 rooms available. And, every prisoner will do the same thing. We, here have to find out that who all will succeed in breaking the prison and who all will not.

The question is merely about logic. The more you will think, the nearer you will reach to the answer. So, try to solve it on your own. There are many versions of this puzzle available on the Internet. So, it is better if you try to solve it on your own. All the best LLs. Don't forget to comment your answers below this post.

Cricket League Puzzle

Hey Logic Lovers!!
I am here with some interesting brain exercise for you today.
This doesn't require any kind of knowledge or interest in the field of cricket. You just need to focus on the facts given and try to answer the questions.
League: IPL(Indian Premier League)
Teams: 8
Number of Games: In the initial stage, every team is supposed to play all other opponent teams twice.
Rules:
There will not be any tie/draw in any game.
Every game will end with a result, ie, one team winning and other team losing.
For every win, two points are awarded.
For every loss, zero points are awarded/deducted.
Top four teams after this initial stage will qualify into the semifinals.
If two or more teams end up with the same number of points, the net runrate will come into picture, and the team with the higher rating will end up above the other team/teams on the point table.

I, being a team manager and interested in statistics want some informations.
1) What is the least number of games a team can win and still be through to semi finals? In other words, I want to find out that at least how many games my team must win to stay hoping for the semi final spot.
2) What is the maximum number of games a team can win and still do not qualify for the semi finals? In other words, even after winning what maximum number of games, other teams can stop my team's way to the semi finals.

You are supposed to answer both the questions with the correct logic(the number of points of all the eight teams - on the point table) Try to answer both but if you find difficulty and can't answer both, you can comment answer of any single question too. Comment your answer and we can discuss on logic behind these kind of puzzles.
All the best Logic Lovers!!! Your brain exercise starts now... Keep puzzling.