what does the below rebus means?

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

A couple went to a hill station to enjoy their vacation. They have 12 sons, and each has a wife who has 3 sons further.

How many people went to the hill station?

A bridge is about to collapse. There are four people P, Q, R and S on one of the sides. Before the bridge collapses, they want to cross it. Now since the bridge is too weak, it can only stand the weight of two people at a time. Also, it is night time and nothing is visible. They have just one torch with them.

Now P takes one minute to cross the bridge, Q takes two minutes to cross, R takes five minutes to cross and S takes ten minutes to cross.

The bridge will collapse in seventeen minutes. How will they be able to cross the bridge before it collapses?

If you say my name, I will no longer exist. What am I?

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

I have Rs.50 and I spend it in the way as below.

What is the next number?

77, 49, 36, 18 ?

You and your two friends are working in a multinational company. How can you three find out the average salary of you all without disclosing your own salary to the other two?