On a game show there are three closed doors – one hides a car and the other two conceal a goat. The contestant selects a door, which remains closed, and the host, knowing where the car is hidden, reveals a goat behind one of the remaining two doors. The contestant is then given the option to switch doors or stay with the one they originally selected. What should the contestant do to have the best chance of winning the car?
The contestant should switch doors, which doubles the chance of winning the car. Initially there is a 2/3 chance of picking a goat, but once the other goat is revealed, switching to remaining door gives the contestant a better chance of winning the car. This is known as the Monty Hall Problem and can be very unintuitive.
A secret lair has a code to only allow members to enter. The person wanting to enter says a random number, then is told a number in response. In order to enter they must say the correct third number. Here are sequences that allowed entrance.
Five because s-e-v-e-n has 5 letters. The first number can be anything, the second number is the number of letters in the first number, and the third number is the number of letters in the second number.