Toggle Lights
GF(2)^5
There are nine lights and six switches. Pressing a switch will toggle the three lights in its row.
You can easily switch all light on. However, not all light patterns can be reached. For example, it is impossible to have exactly one light on.
Hammingcode
There are four switches for seven lights. Each switch toggles the lights to which it is connected by a line. Although the circuit is so simple, there is a puzzling effect: at least three lights will burn, unless all of them are off.
Such configurations are used in information technology to detect and correct errors in data-transmission.
Petersengraph
The figure shown here is called Petersen’s graph. Using the buttons, you can generate a path through all its nodes.
However, it is impossible to find a closed path with that property.
