Half-way up the hill, I see thee at last, lying beneath me with thy sounds and sights — A city in the twilight, dim and vast, with smoking roofs, soft bells, and gleaming lights.
Given a corked bottle with only a penny inside, how can you remove the penny without pulling out the cork, breaking the bottle and leaving the cork intact?
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.
You have two buckets. One holds exactly five gallons and the other three gallons. How can you measure exactly four gallons of water into the five gallon bucket?
Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.