John Heysham Gibbon was most renowned surgeon of 1940-1970. More than 90% of his surgeries he performed are highly successful and still almost all of his patients die.

The surgery was performed way back, by now approx 90% of them have died by old age.

A man owned a casino and invited some friends.
It was a dark stormy night, and they all placed their money on the table right before the lights went out.
When the lights came back on, the money was gone.
The owner put a rooster in an old rusty tea kettle.
He told everyone to get in line and touch the kettle after he turned the lights off, and the rooster will crow when the robber touched it.
After everyone touched it, the rooster didn't crow, so the man told everyone to hold out their hands.
After examining all the hands, he pointed out who the robber was.
How did he know who stole the money?

Because the tea kettle was rusty, whoever touched it would have rust on their hands. The robber didn't touch the kettle, therefore he was the only one whose hands weren't rusty.

What is the least number of people that need to be in a room such that there is greater than a 50% chance that at least two of the people have the same birthday?

Only 23 people need to be in the room.
Our first observation in solving this problem is the following:
(the probability that at least 2 people have the same birthday + the probability that nobody has the same birthday) = 1.0
What this means is that there is a 100% chance that EITHER everybody in the room has a different birthday, OR at least two people in the room have the same birthday (and these probabilities don't add up to more than 1.0 because they cover mutually exclusive situations).
With some simple re-arranging of the formula, we get:
the probability that at least 2 people have the same birthday = (1.0 - the probability that nobody has the same birthday)
So now if we can find the probability that nobody in the room has the same birthday, we just subtract this value from 1.0 and we'll have our answer.
The probability that nobody in the room has the same birthday is fairly straightforward to calculate. We can think of this as a "selection without replacement" problem, where each person "selects" a birthday at random, and we then have to figure out the probability that no two people select the same birthday. The first selection has a 365/365 chance of being different than the other birthdays (since none have been selected yet). The next selection has a 364/365 chance of being different than the 1 birthday that has been selected so far. The next selection has a 363/365 chance of being different than the 2 birthdays that have been selected so far.
These probabilities are multiplied together since each is conditional on the previous. So for example, the probability that nobody in a room of 3 people have the same birthday is (365/365 * 364/365 * 363/365) =~ 0.9918
More generally, if there are n people in a room, then the probability that nobody has the same birthday is (365/365 * 364/365 * ... * (365-n+2)/365 * (365-n+1)/365)
We can plug in values for n. For n=22, we get that the probability that nobody has the same birthday is 0.524, and thus the probabilty that at least two people have the same birthday is (1.0 - 0.524) = 0.476 = 47.6%.
Then for n=23, we get that the probability that nobody has the same birthday is 0.493, and thus the probabilty that at least two people have the same birthday is 1.0 - 0.493) = 0.507 = 50.7%. Thus, once we get to 23 people we have reached the 50% threshold.

A man is sitting in a pub feeling rather poor. He sees the man next to him pull a wad of £50 notes out of his wallet.
He turns to the rich man and says to him, 'I have an amazing talent; I know almost every song that has ever existed.'
The rich man laughs.
The poor man says, 'I am willing to 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, Joanna Armstrong-Miller?'
The rich man goes home poor. The poor man goes home rich.
What song did he sing?

A man was found dead with a cassette recorder in one hand and a gun in the other.
When the police came in, they immediately pressed the play button on the cassette.
He said "I have nothing else to live for. I can't go on," then the sound of a gunshot.
After listening to the cassette tape, the police knew that it was not a suicide, but a homicide.
How did they know?

If the man shot himself while he was recording, how did he rewind the cassette tape?

A man is found murdered on a Sunday morning. His wife calls the police, who question the wife and the staff, and are given the following alibis: the wife says she was sleeping, the butler was cleaning the closet, the gardener was picking vegetables, the maid was getting the mail, and the cook was preparing breakfast.
Immediately, the police arrest the murdered. Who did it and how did the police know?

One winter day, there was a man standing in the middle of someone's front yard. The person stayed there for several weeks without moving and the owner of the yard didn't mind. Eventually the man left. Who was the man?

Galaxy Detective Karamchand was on a case. A spaceship was lost. Her partner, Galaxy Junior Detective Brightstar gave her a piece of paper.
This was the location of the spaceship! This is what the slip had scribbled on it: Juice, Umbrella, Potato, Ice, Tomato, Elephant, Rice.
Where is the spaceship?

The front of me is the source of a song
Or to kiss with a fervor of love lifelong.
My back is a plant fit for a queen,
Crafted by needle, chemical, or machine.

If will follow you for 1000 miles but not miss home. It desires neither food nor flowers. It fears not water, fire, knives, nor soldiers. But it disappears when the sun sets behind the western mountains. Who Am I?