At the market you can buy a cow for $10, a pig for $1 and 8 hens for $1. How many animals would you need to buy to get 100 mixed animals for exactly $100?
7 cows, 21 pigs and 72 hens. The trick to this is finding the combination of cows and hens with the same cost and quantity since pigs are already equal. The magic combination is 7 cows and 72 hens, giving you 79 animals that cost $79 ($70 + $9). Then you just add 21 pigs to get to 100 animals.
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.
I’m in an elevator with two other people. When it reaches the first floor, one person gets out and six get in. When it reaches the second floor, three people get out and twelve get in. At the third floor, five leave and nine enter. It rises to the fourth floor, one person gets on and the doors close. Suddenly, the elevator cable snaps and the car smashes to the ground. No one survives the fall, yet I’m alive and know exactly how many people go on and off the elevator at every floor. How is this possible?
A traffic light. It has three “eyes” (the red, orange and green lights) and the leg is the pole holding it up. Many people beg the light to stay green as they’re approaching.