A man is running across a field at night clutching something in his arms as several other men pursue him. He looks back and sees they’re getting closer. In a final burst of effort his pursuers catch up and bring him crashing to the ground. His pursuers stand over him but do not touch him or take what he was carrying. Why not? Who was the running man?
A harvest sown and reaped on the same day
In an unplowed field,
Which increases without growing,
Remains whole though it is eaten
Within and without,
Is useless and yet
The staple of nations.
You’re waiting to board your flight at the airport with 99 other passengers, each with an assigned seat. All but one of the passengers will gladly sit in their designated seat. The only exception is Randall, a scoundrel who refuses to follow the rules. When he boards, he will choose a random, unoccupied seat.
If a rule-following passenger finds someone in their spot, they will choose another one at a random from the remaining unoccupied seats.
What is the probability that the last person to board the plane will sit in their proper seat?
The randomness stops as soon as someone else sits in Randall’s assigned seat. The chances of this happening range from 1 out of 99 to 1 out of 1 (when only one seat remains).
Thus, the probability of the last person sitting in their own seat can be calculated as 1/99 plus the sum of 2 to 98 of the formula 1 / n × (n + 1), which works out to 0.5, or 50%.
So there’s a 50% chance the last passenger will sit in their own seat thanks to Randall for screwing up order and procedure when boarding an aircraft.
A wise king devised a contest to see who would receive the Princess’ hand in marriage. The Princess was put in a 50 x 50 foot carpeted room. Each of her four suitors were put in one corner of the room with a small box to stand on. The first one to touch the Princess’ hand would be the winner and become the new King.
The rules were the contestants could not walk over the carpet, cross the plane of the carpet, or hang from anything; nor could they use anything but their body and wits (i.e. no magic, telepathy, nor any items such as ladders, block and tackles etc). One suitor figured out a way and married the Princess and became the new King. What did he do?