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.

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

Assume the given figure to be a delicious doughnut. Yes, now you can concentrate more on the puzzle. So you have this delicious doughnut in your refrigerator when your friends come knocking at the door. There are eight of them. Now you have to make three cuts in this doughnut so that each one of you nine people can enjoy a piece of it. Neither you nor your friends would mind the size of their piece as long as they are getting it. How will you do it?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?

What do you see in the image below

The more you take me, the more you leave me behind.
Who Am I?