## Math

A few riddles have caught my attention to a level that I've remembered them for years.

- You have a set of 13 coins, and one of them is a counterfeit. The counterfeit coin is slightly lighter or heavier than the other coins, which all have the same weight. You can compare the masses of coins using a balance with two weighing plates, and the balance tells which side is heavier (or whether both are equal). Determine how to find the counterfeit coin with only 3 discrete uses of the balance.
- Four prices (that is, positive numbers with two figures after the decimal point) have a sum of 7.11 and also a product of 7.11. Find the four prices.

## Mechanical

- The left bicycle pedal is commonly installed with a counterclockwise screw thread. But if you think about the torque from the pedal rotation, this seems to be the wrong choice. Why is the counterclockwise thread used here?