What is always in front of you but can’t be seen?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

If six children and two dogs were under an umbrella, how come none of them got wet?

The more of this there is, the less you see. What is it?

Sally lives in a place where six months of the year is mild summer and the temperature drops significantly the other six months. She owns a lake where there is a small island. She wants to build a house on the island and needs to get materials there. She doesn’t have a boat, plane, or anything to transport them to the island. How does Sally solve this problem?

What always comes into a house through the keyhole?

There is a square piece of paper with a hole that is denoted by the circle on the top right side in the given picture. You have to cut the paper in a manner that it forms two and only two separate pieces of paper and then rearrange the pieces in a manner that the holes come in the centre of the paper.

Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation. Conditions: Each must be used exactly once and no other numbers or symbols can be used.