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.
Ten seconds is 1/6 of a minute and 1 minute is 1/60 of an hour, so 10 seconds is 1/360 of an hour.
If you graph her trip with the speed on the y-axis and the time on the x-axis, you get a triangle with height of 60 mph and width of 1/360 of an hour. To calculate the area of the triangle, you multiply 1/2 × 1/360 × 60 = 1/12.
Chuck and Ruby were going to meet at a hotel for their anniversary dinner, but Ruby didn’t show. Chuck was angry and left her a passive aggressive message on their kitchen table in the form of fifteen matchsticks spelling “hotel” and went to bed. When Ruby got home and saw the matchsticks, she removed one and went to bed. When Chuck woke up the next morning and saw Ruby’s new message, he realized his mistake. Which stick did Ruby remove and what was the new message?
Ruby had removed the top of the T and the new message could be seen upside down from where Chuck sat at his breakfast of sadness and anger. What he saw was 7 3 1 0 4, or 7/31/04, the date of their anniversary. In his excitement, Chuck had gone to the restaurant a day early, on July 30th. All was forgiven by both parties and Chuck and Ruby had a wonderful dinner together. They also promised to buy a whiteboard for the kitchen so they wouldn’t have to use matchstick messages ever again.
