I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

I had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?

Rearrange the letters in "new door" to make one word.

You want to boil a two-minute egg. If you only have a three-minute timer (hourglass), a four-minute timer and a five-minute timer, how can you boil the egg for only two minutes?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, "Why are you smiling?"

How did he know his companion was smiling?

Find three numbers such that

* When we multiply three numbers, we will get the prime numbers.
* The difference between the second and the first number is equal to the third and second.

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

If 21x = 79x, what is the value of x?

If there are fifteen crows on a fence and the farmer shoots a third of them, how many crows are left?