What is both possible and impossible at the same time?

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:

Door A: It's behind B or C
Door B: Its behind A or D
Door C: It's in here
Door D: It's not in here

Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

Your last good ping-pong ball fell into a narrow metal pipe embedded one foot deep in concrete.
How can you get it out undamaged, if all the tools you have are your tennis paddle, shoe laces, and plastic water bottle, which does not fit into the pipe?

You can win me and lose me but never buy me
You can not eat me and never want to part with me
I can make you cry or bring you joy
I am not a machine and definitely not a toy
You keep me but i am not forever just yours
You might find me in a case or on a shelf next to a vase
I am hard and i am tall if you bump me i am sure to fall
I am made of different materials and am at many events
If your lucky and fight hard I might be yours
What am I ?

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

Chocolate costs 6 rupees and a Toy costs 5 rupees. If you have 32 rupees in total, how many chocolates and how many Toys can be purchased with that amount?