A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.
Now all your friends have one apple each, yet there is an apple remaining in the basket.
How?

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

A mad serial killer kidnaps people and forces them to play the game of 2 pills with them, In this game, there are pills in the table and one of them is normal pill while the other one is deadly poisonous.
The victim will choose one pill and the killer will pick the other pill and both simultaneously will swallow the pill with water.
victim dies every time.

One day the serial killer kidnaps the Joseph and forces him to play the same game with him.

Joseph solves the mystery of the two pills and remains alive.

Explain?

By what process could you make a 'Tea-Table' into food?

A man is sitting in a bar when a rich man sits next to him. He turns to the rich man and says, “Did you know I know almost every song that has ever existed?”

The rich man laughs. The man then says, “I bet you all the money you have in your wallet that I can sing a genuine song with a lady’s name of your choice in it. The rich man laughs again and says, “OK, how about my daughter’s name, Jamie Armstrong-Miller?” Minutes later, the man collects his cash and the rich man goes home cashless. What song did the man sing?

People are waiting in line to board a 100-seat aeroplane. Steve is the first person in the line. He gets on the plane but suddenly can't remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it's available, otherwise, they will choose an open seat at random to sit in. The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?

What can jump higher than a building?

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?