Tools for Logical Thinking

Last updated Aug 9, 2024 Edit Source

A toolbox for solving problems

The problem goes: There is a room with a light bulb behind a closed door. Outside, there are 3 switches. You can flip the switches however you want, but once you open the door, you cannot flip the switches anymore. Figure out which switch is connected to the light bulb.

At first I thought this was some variant of the Monty Hall problem. However, there is a 100% probability solution to this.

n = input variables S = output states To uniquely determine which input is mapped to which output state, $S \ge n$ The go-to method is multiple measurements, but we cannot do that here:

• (1, 0, 0): Off
• (1, 1, 0): Off
• (1, 1, 1): On implied

In the light example, there are 3 inputs. As long as we can only view 2 states, any 2 inputs might lead to one of the states. The key insight is to increase the number of states:

• On
• Off but warm
• Off but cold After, it is a matter of figuring out what type of experiments can create these new states.