I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.
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.
You are confined in a room and given two metal rods. Out of these two rods, one is magnet and the other is the iron rod. They look starkly similar. You don't have any other metal object in the room.
In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki