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.
Shawn and Kyle are bunk mates in prison and are desperate to escape. There is an unbarred window high above them, but the walls are smooth and it’s too high for them to reach even when standing on each other’s shoulders. Their cell has no furnishings other than a toilet and even when standing on the toilet and each other’s shoulders, they can’t reach the window.
They’ve tried digging through the dirt floor but the wall extends 50 feet below. How could escape through the window?
They could dig down with their hands, but it would take too long to dig 50 feet down. Instead, they could pile the dirt they dig up to give them enough height to reach the window. If they put the toilet seat down, they could pile the dirt on top, then get on each other’s shoulders to reach the window. That would mean only one of them would be able to get out. The remaining prisoner could either continue piling dirt to account for the missing guy or the escaped prisoner could come back with a rope to help his mate escape.
Two children were playing checkers and each played five games. Both children won the same number of games yet there were no ties. How is this possible?
You are a cook in a remote area with no clocks or other way of keeping time other than a four-minute and a seven-minute hourglass. On the stove is a pot of boiling water. Jill asks you to cook a nine-minute egg in exactly 9 minutes, and you know she is a perfectionist and can tell if you under cook or overcook the egg by even a few seconds. How can you cook the egg for exactly 9 minutes?
1. Flip both hourglasses over and drop the egg into the water. 2. When the 4-minute timer runs out, flip it over (4 minutes elapsed, 3 remaining on the 7-minute timer). 3. When the 7-minute timer runs out, flip it over. (7 minutes elapsed, 1 remaining in the 4-minute timer) 4. When the 4-minute timer runs out, flip the 7-minute timer over. (8 minutes elapsed. 6 minutes remained in the 7-minute timer, but flipping it over leaves one minute’s worth of sand on top. When it runs out exactly nine minutes will have elapsed.)
