# Math

## Resistor Cube Solution

The problem quickly becomes very complex if the usual parallel and series resistor equations are used. It can be done, but there are easier methods. It is quite simple if symmetry is invoked. Suppose a current of 3 A flows through the supply leads. Since the cube has a 3-fold symmetry about rotations through the …

## Solution to the Scales and Counterfeit Coin Problem

The steps necessary to solve the problem depend on the results of each use of the scales. Thus the solution quickly becomes very complicated if mapped out with numbers. Therefore, I present an more abstract solution first and then add the numbers later. There are four points to solving the problem: Let us consider families …

## The Scales and the Counterfeit Coin

This problem was given to me many years ago by my friends Heather and Ross. You have a bag of 117 coins of which 1 is a counterfeit. This counterfeit is identical to the other coins except that it is slightlyheaver or lighter than the real coins. You do not know which. You are given …