Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

In an office's desk, you find a unique method that shows the current day of the month. Two numbered cubes are used to depict the current date.

Can you find out the numbers on both the cubes so that each date can be mentioned using them?

Please note that you have to use both the cubes to display any date. Thus the 1st day must be represented by 01 and so on.

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

What does the following represent?

N N N N N N N

A A A A A A A

C C C C C C C

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

You have $100 with you and you have to buy 100 balls with it. 100 is the exact figure and you can't go below or above the numbers and you have to use the entire $100. If there is no kind of tax applied how many of each of the following balls will you be able to buy:

Green Balls costing $6
Yellow Balls costing $3
Black Balls costing $0.10

Now, how many of each must you buy to fulfil the condition given?

Solve the maths equation in the picture below by placing the numbers 1 through 9 into the boxes so that all the 3 equations are correct.

There are four people in a house. A fireman, an athlete, an old woman, and a drunk guy. The house catches fire and before the fact is known, it is too late. All they know is that the entire house is in flames and it will collapse exactly after twelve minutes. Now they can move out of the house but for that, they will have to pass the hallway which is entirely blazing with flames. Thus to move, one must carry a fire extinguisher to keep the flames away. Seeking the burnt wooden floor, only two people can run through that hallway at one time. But for others to go, one must return back with the fire extinguisher. The fireman is trained for such tasks and can run through the hallway in a minute. The athlete can make it in a couple of minutes. The old woman can run slowly and will cover the hallway in four minutes. The drunk guy will take five minutes to run through it. If all of them can make it through the hallway in twelve minutes, all of them will be saved. When two move together, they will run at the speed of the slower ones.

How will all four of them manage to run to safety?

I have a sore throat and a severe headache. I have four tablets with me that are identical to each other and they do not have any cover on them. There is no way I can identify which tablet serves what purpose. The only thing that I know is that two of these four tablets are for the throat and the remaining two are for the headache. To treat my condition, I must take 1 of each. What will I do now?

In a university, a professor gave a set of three problems to the three brilliant students of his class. See the image for the questions.