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?

A man started to town with a fox, a goose, and a sack of corn. He came to a stream which he had to cross in a tiny boat. He could only take one across at a time. He could not leave the fox alone with the goose or the goose alone with the corn. How did he get them all safely over the stream?

Can you spot what's wrong with the following sentence?

PETER WAS ANGRY AT
HIMSELF BECAUSE HE
ACCIDENTALLY LEFT THE
THE KEYS TO HIS CAR
AT HIS FRIEND'S HOUSE.

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

It can be easily calculated that the digits 0 to 9 can be arranged into 3628800 distinct ten-digit numbers.

But do you know how many of these numbers are prime?

I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

How many sides does a circle have?

I get hot but I never sweat,
I cook food but I am not a chef,
I have a door but you can't enter me,
I have a light but I am not a lamp.
Who am I?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

How can you take 2 from 5 and leave 4?