A painter needed 3 days to paint a room. How long would it take him, working at the same rate, to paint a room twice as large (twice the width and twice the height)?
12 days because the walls would be four times as big as the first room.
If the walls are 10 ft x 10 ft, then each wall has 100 square feet. Adding the four walls makes 400 square feet to paint. Doubling the width and height of the walls to 20 ft x 20 ft means each wall is now 400 square feet, for a total of 1600 square feet to paint. 1600 ft is four times 400 square feet, thus if it took him 3 days to paint 400 square feet, it will take 12 days (or four times as much) to paint 1600 square feet.
You are decorating for spring and you’ve found a bargain. A huge box of beautifully decorated tiles, enough to provide a border in two rooms. You really can’t figure out how to arrange them. If you set a border of two tiles all around, there’s one left over. If you set three tiles all around or four or five or six there’s still one tile left over. Finally you try a block of seven tiles for each corner and you come out even. What is the smallest number of tiles you could have to get this result?
Ralph goes to the hardware store to buy something for his house. He asks the clerk how much one will cost and the clerk looks it up and tells him it will be $3. He asks about buying twelve and is told it will be $6. Two hundred will cost $9.
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.