Lights Out

Lights Out was a Tiger Electronics handheld toy from 1995. The math behind it is gorgeous — the entire puzzle reduces to linear algebra over GF(2) (binary), and there's a deterministic solving algorithm.

The "chase the lights" technique

The fastest manual solving method: click any cell on the bottom row to turn off the light directly above it. Repeat across the bottom. Now the top 4 rows have a specific pattern that determines the first row's solution. With practice, most puzzles solve in under 30 seconds.