1. You are standing outside of a room with no windows. The room has three light bulbs and three switches outside of the room. Each switch controls one of the light bulbs. You may only enter the room one time. How can you find out what switch goes to each light bulb?

Solution:
To find out what switch goes to what light bulb, you could turn on the first switch and wait five minutes. After five minutes have passed, turn off the first switch and turn on the second switch.
Look for the warm light bulb when you walk back into the room. The light that is on goes to the second switch, the warm light bulb goes to the first switch and the last light bulb goes to the third switch.

2. You have a 3-gallon jug and 5-gallon jug, how do you measure out exactly 4 gallons?

Solution:

  1. First, fill the 3-gallon jug. Then pour the 3 gallons into the 5-gallon jug.
  2. Now the 3-gallon jug is empty, and the 5-gallon jug has 3 gallons in it.
  3. Fill the 3-gallon jug again and pour into the 5-gallon jug. Only 2 gallons will fit because it already has 3. Exactly 1 gallon is left in the 3-gallon jug.
  4. Dump out the 5-gallon jug.
  5. Pour your 1 gallon into the 5-gallon jug. Fill up the 3-gallon jug one more time and pour it into the 5-gallon jug. You have exactly 4 gallons!

3. You͛re about to get on a plane to Seattle. You want to know if it͛s raining. You call 3 random friends who live there and ask each if it͛s raining. Each friend has a 2/3 chance of telling you the truth and a 1/3 chance of messing with you by lying. All 3 friends tell you that ͞Yes͟ it is raining. What is the probability that it͛s actually raining in Seattle?

Solution:
You only need 1 of your friends to be telling the truth for it to be raining in Seattle. It͛s fastest just to calculate the odds that all ϯ are lying, and it͛s not raining. Each friend has a ϭͬϯ chance of lying. Multiply the odds together… you get 1/27 (1/3 * 1/3 * 1/3).
So 1/27 is the probability that all 3 friends lied at the same time. The probability that at least 1 told you the truth? 26/27 or around a 96% that it͛s raining in Seattle.