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.
I stretch as far as a football field, Yet I fit in the palm of your hand. I will make you bleed if you don’t use me often. You put me in your mouth but don’t eat me, Then you throw me away.
Floss. It typically comes in 100 yard packs, which fit easily in your hand. If you don’t floss regularly, your gums will bleed. You use floss in your mouth then throw it away when you’re done.
It’s against the rules for you to play fair, I always win but you don’t care, I’ve ruined lives and crushed dreams, But the allure is too much it seems.
A casino. If you use methods to make the odds more fair to you, they kick you out. The house always wins, yet people continue to play. Gambling has ruined countless lives and crushed dreams of making millions, but the hope of winning continues to draw people in.
You must buy 100 chickens for exactly $100, and purchase at least one chicken from each store. The first store charges 5 cents/chicken, the second charges $1/chicken and the third charges $5/chicken. How many chickens should you buy from each store?
1. Each letter represents a different digit from 1 to 9 2. The total of each row is 17. 3. (B × B) + B + F = A 4. C × F = EF (a 2-digit number, not their product)
A + B + C = 17 D + E + F = 17 B2 + B + F = A C × F = EF
To begin with, B has to be a 1 or 2 or else A wouldn’t be a single digit. Plug in B = 2, gives you 6 + F = A, meaning F and A can only be (1,7) or (3,9). To get 17, C would have to be 8 or 6, but those values don’t work for C × F = EF. So B must be 1.
2 + F = A means F and A can be (2,4), (3,5), (4,6), (5,7), (6,8) or (7,9). To get 17 on the top row, the only option that leaves C as a single digit is F = 5 and A = 7.
C × F = EF 9 × 5 = 45, so E = 4 and D = 8 to make the second row equal to 17.