Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

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?

Find the next number in the series.
1 10 24 43 67 ?

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?

I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number:

First digits is divisible by 1.
First two digits are divisible by 2.
First three digits are divisible by 3.
First four digits are divisible by 4.
First five digits are divisible by 5.
First six digits are divisible by 6.
First seven digits are divisible by 7.
First eight digits are divisible by 8.
First nine digits are divisible by 9.
The number is divisible by 10.

Can you find out the number ?

Two guards were guarding the camp.Guard-1 was looking towards the south to make sure no threat is coming from the road.Guard-2 was looking at the north to make sure no threat is coming from the top. Suddenly Guard-1 ask the Guard-2 why he is smiling?How Guard-1 knows that Guard-2 is smiling?

A donkey is behind another donkey
I'm behind that second donkey
But there is a whole nation behind me

It is a murder you can describe in a word.

There was a kingdom in which the king had no heir to take over his thrown. Even the queen was dead and he himself was on the verge of dying. He thought about it and then summoned all of the teenagers. He gave one seed each to all of them and asked them to grow the plant. He announced that the one with the most beautiful plant will become the king/queen of the empire after the death of the king.

After a month, all of them were called. The king looked at all of the plants but announced the girl with an empty pot as the queen of the empire. Why?

There are two beautiful yet remote islands in the South Pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.
You are on one of the islands and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.
Can you guess what the third Islander will answer to the same question?

Spot 5 differences in two Christmas tree below: