Here is a mathematical expression that also secretly tells a movie name. What movie is that?

What kind of tree can you carry in your hand?

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

Which five letter word can be added at the end of below word to form a
valid word?

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What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?

Can you find the mistake in the below statement?

A Shopkeeper sold a few chickens to four different customers on a particular day. It was such that each customer purchased half of the remaining chickens and half the chicken more.

Can you find out how many chicken were sold by the shopkeeper on that day if we tell you that the fourth customer bought a single chicken ?

There was a minor accident with a doctor's son but the doctor noticed no major injury. After the treatment, the father of that doctors son is sitting with the son of the doctor without the doctor being in the room.

How can this be possible?

If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?