How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

Four cars come to a four-way stop, each coming from a different direction. They can’t decide who got there first, so they all go forward at the same time. All 4 cars go, but none crash into each other. How is this possible?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

A man was telling some of his war stories to his grandchildren.
"When the World War I was on the verge of end, I was awarded for my bravery for I had saved a group of my men." He coughed and then added, "When we were fighting in northern France, an enemy soldier threw a grenade at us. Before it could explode, I picked it up and threw it away. For my act of bravery, right before the war ended, A General gave me a sword engraved with the words "Awarded for Display of Bravery and Heroism in World War 1"."

Hearing this, one of the grandson spoke up. "Grandpa, this is not a true story. It can"t be true!"

The truth is that it was not. How did the grand children know it?

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

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

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

Find the next number in the following series:
6, 14, 26, 98, __?

Consider all the numbers between 1 and 1 million. Among all these numbers, there is something very special about the number 8 and the number 2202. What is it?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?