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.
Five hundred begins it, five hundred ends it, Five in the middle is seen; First of all figures, the first of all letters, Take up their stations between. Join all together, and then you will bring Before you the name of an eminent king.
A six-digit number represented by ABCDEF (each letter represents a different number) can be multiplied by 2, 3, 4, 5, and 6 and yet no new digits appear in the result. As a matter of fact, all the digits are rotated. What is the number?
I harvest you, though you’ve no grain, I reap you in the wind and rain, You bleed not but your soft meat And nectar makes a sweetest treat. What am I?
A clam or oyster. You harvest clams or oysters on the beach or go diving, and the beach is often windy and rainy. Neither bleeds but are known for having, soft, slimy meat, and people often drink the “clam nectar” or “oyster juice”.
The letter ‘b’, the verb to be or a bee. The letter b and a bee are both small and to be means you exist. Bees make honey, which is sweet, and their wings are going at around 230 beats per second. Bees are valuable because they pollinate flowers. They live in hives and the queen bee runs the show. If it weren’t for bees, we would probably starve to death.
A word with horizontal symmetry is one whose letters are a mirror image of themselves. If you drew a horizontal line across the word and folded it over, it would overlap on itself. For example, EXCEEDED and ICEBOX have horizontal symmetry, but VERTICAL and SIMPLE do not.
What is the longest word with horizontal symmetry?