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.
The half bucket of dimes. It might be tempting to say they’d be worth the same, since a nickel is worth half as much as a dime. This would be accurate if they were the same size, but the dime is smaller. Thus more dimes would fit in the same space, resulting in more value for you, you lucky dog.
The answer to each clue is a single, 100-point word, or a word whose letters add up to 100, with a = 1, b = 2. I wrote this word value calculator so you can easily check your guesses.
i. Peanut butter tastes like this. ii. The hat a Dad wears. iii. To fire a chef, iv. A smart timepiece. v. Figured it out again. vi. Where a kid can sleep. vii. The magical fruit leaves you doing this. viii. Betrayed for this much silver. ix. A baked good that is height challenged. x. A sticky way to neaten your hair.
Franklin. It’s a list of the men on U.S. currency, $1, $2, $5, $10, $20 and $50. The $100 bill has Franklin. And an interesting tidbit is that Hamilton, along with Franklin, are the only two men in the list who did not serve as president.