You have a balance scale and six weights. What is the fewest number of times you need to use the balance scale in order to positively identify the heavier weight in each pair?

You have two small cups filled with water and an empty bucket. How can you dump all of the water out of the cups and into the bucket and tell which water came from which cup, without using any dividers of any kind?

You have a committed a terrible crime and tomorrow morning you will be taken to the town square and executed. The executioner has taken a liking to you and decides to do you a favor and allow you a choice ...