Problem of the Week - 9/19

King Hiero II is calling on Archimedes again. This time, he is having a problem with his tax collection. He has received 20 bags of gold from his people, but he suspects one bag may be light, meaning that someone is cheating on their taxes! Now Archimedes has to test the bags of gold using the only scale in the land: the Doomsday scale! This scale is built using one of Archimedes' simple machines: the lever, and looks like this:

This means the scale can only show if one side is heavier than the other. Therefore, Archimedes must always weigh an equal number of bags on both sides. However, there is a catch. The scale is not called the Doomsday scale without reason! If Archimedes uses the scale more than three times it will self-destruct, taking everyone with it. How can Archimedes find the phoney bag of gold using only three measurements?


MORE RESOURCES

---

To learn more about Archimedes famous experiment with King Hiero II's golden crown, check out these websites:

Introduction to the story of the crown
Did Archimedes really use a bathtub?