Physics
Physics
Problem
You are supplied with four identical resistors. Explore how many different total resistances you can make using some or all of the resistors.Intuitive explanation
The key insight is that resistors combine in fundamentally different ways depending on how you wire them: series resistances add directly, while parallel resistances combine reciprocally. By systematically trying different configurations—using 1, 2, 3, or all 4 resistors in various series and parallel arrangements—you'll discover that the same total resistance can often be achieved multiple ways. The challenge is to find every distinct value possible, not just count configurations.
Intuitive explanation
The key insight is that resistors combine in fundamentally different ways depending on how you wire them: series resistances add directly, while parallel resistances combine reciprocally. By systematically trying different configurations—using 1, 2, 3, or all 4 resistors in various series and parallel arrangements—you'll discover that the same total resistance can often be achieved multiple ways. The challenge is to find every distinct value possible, not just count configurations.