You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls and instructs you to divide the 100 marbles into the two bowls. You can divide them however you want as long as all the marbles are in the bowls. You will be blindfolded and the bowls and marbles will be thoroughly mixed. You will then choose a single marble from one of the bowls. If the marble is white, you live. Black and you will be put to death.
How do you divide the marbles up so that you have the greatest probability of choosing a white marble?
Place one white marble in one bowl and place the rest of the marbles in the other bowl (49 whites, and 50 blacks).
This way you begin with a 50/50 chance of choosing the bowl with one white marble and living. Even if you choose the other bowl, you still have an almost 50% chance of picking one of the 49 white marbles. There are no guarantees in life, but this gives you the best change of surviving.
Two bikes are traveling toward each other at a constant speed of 10 mph. When the bikes are 20 miles apart, a bee flies from the front wheel of one of the bikes toward the other bike at a constant speed of 25 mph. As soon as it reaches the front wheel of the other bike, it immediately turns around and flies at 25 mph toward the first bike. It continues this pattern until the two bikes smush the bee between the two front tires.
The easiest way to think about this is to consider the time. The bikes will take 1 hour to touch, given that they start 20 miles apart and are each traveling toward each other at 10 mph.
Therefore the bee is buzzing back and forth at 25 mph for 1 hour.
She will always need to give you 5 apples. You both need at least 5 apples to begin with, but apart from that it doesn’t matter exactly how many you each have. When she gives you 5 you will have 10 more than her because she will lose 5 and you will gain 5, resulting in a net difference of 10.
For example, if you each have 25 apples and she gives you 5 of hers, she will be left with 20 and you will now have 30, precisely 10 more than she has.
It’s true I bring serenity,
And hang around the stars
But yet I live in misery;
You’ll find me behind bars
With thieves and villains I consort
In prison I’ll be found
But I would never go to court,
Unless there’s more than one