Laser and mirror puzzles

A laser fires, you set mirrors to bend the beam, and it has to reach a target. The idea has been around since the 1980s and it still holds up. Beamzag is my daily take on it. This page covers how the beam behaves, where the idea comes from, a few versions you can still play, and how to get better at them.

How the beam behaves

Nearly all of these puzzles share the same physics. A mirror sits on the diagonal of a square and turns the beam by a right angle. A beam travelling to the right turns up when it meets a / mirror and down when it meets a \. Most digital versions let both faces reflect, so it never matters which side the beam hits. The rest is up to the designer: targets the beam has to pass through, blocks that stop it, splitters that make two beams out of one, and in Beamzag, a fixed number of mirrors that all have to be used.

Where it comes from

Deflektor came out in December 1987 for the ZX Spectrum, Commodore 64, Amstrad CPC and other home computers. Costa Panayi designed it at Vortex Software and Gremlin Graphics published it. You rotate mirrors against a time limit to steer a beam onto every target on the screen, without letting it sit too long on anything that overloads the system.

Khet turned the idea into a two-player board game. It began as a class project at Tulane University and went on sale in 2005 under the name Deflexion. On your turn you move or rotate one mirrored piece, then fire your own laser and try to hit the other player's pharaoh.

ThinkFun's Laser Maze (2013) is the solo version most people know. It uses a real laser and 60 challenge cards from beginner to expert, with mirrors, beam splitters and targets set out on a small grid. Luke Hooper, one of Khet's inventors, came up with it, and four-time World Puzzle Champion Wei-Hwa Huang wrote the challenges. Each challenge has one solution, printed on the back of its card.

Simon Tatham's free puzzle collection has a different kind of mirror puzzle called Undead, and it runs in the browser. The mirrors are already in place, and you fill the other squares with ghosts, vampires and zombies. Numbers around the edge say how many monsters can be seen from there. Ghosts only show up in a mirror and vampires only when you look straight at them, which is where the trouble starts.

Getting better at them

• Start from both ends. The laser fixes how the beam starts and the target fixes how it has to arrive, so the real puzzle is usually in the middle.
• Count turns. Each mirror the beam meets swaps it between moving sideways and moving up or down. If every mirror turns the beam once, three mirrors means a beam that starts out sideways has to finish going up or down.
• Find the squares the beam can never reach. A mirror there does nothing, and on a board with a fixed mirror count it is a mirror wasted.
• Read the obstacles. A wall in an odd spot is often there to close off the short way round.

A new one every day

Beamzag is a free laser-and-mirror puzzle with a new board every day. You get a grid, a laser, a socket and an exact number of mirrors, and the beam has to light every gem on its way into the socket. A solver checks each board before it goes up and rejects any with more than one answer, so you never have to guess. The week starts with a 5×5 and three mirrors and builds to a 9×9 with seven on Saturday, and on Sundays two lasers share the same tray. The how to play page walks through a small board step by step.

For daily puzzles of other kinds, there is a short list of daily logic puzzles like Clues by Sam.