Light, mirrors and switches
Puzzles about steering a beam with mirrors are an old favourite. Prism adds colour that mixes the way real light does. Red, green and blue are the primaries. Red and green make yellow, red and blue make magenta, green and blue make cyan, and all three make white. Paint works differently, so it takes a moment to adjust. With light, mixing always adds. A target that needs white needs all three beams to reach it.
The most useful thing to know is that every piece you can turn has only two positions. A tap flips a mirror or splitter between its two diagonals. So the board is really a set of switches. Your job is to find the right setting for each one. Turning a piece twice just puts it back, so par is simply the number of pieces, or linked groups, that start in the wrong position.
Trace forward, then work back
Begin at each source. Follow its beam to the first piece it meets. Two rules cover every mirror:
- A mirror leaning like a forward slash sends a beam moving right upward, and a beam moving left downward.
- A mirror leaning the other way sends a beam moving right downward, and a beam moving left upward.
At each piece, ask which of the two exits leads anywhere useful. Often one of them runs straight into a wall or off the board. That settles the piece. Keep going until the beam reaches a target or a choice you can't settle yet.
Then switch ends. Look at each target and the colours shown on its rim. List the beams that could reach it and the pieces that would have to steer them. A target that needs magenta must catch both a red and a blue beam. If only one piece can send blue into it, that piece is decided.
Here is the first hand-made level as an example. A red source on the left fires along the top row into a mirror in the top-right corner. The red target sits in the bottom-right corner. As dealt, the mirror leans like a forward slash, so it sends the beam upward and off the board. One tap tips it the other way. The beam now turns down the right edge and lights the target. Every harder level is this same question, repeated and linked together.
Splitters, links and stray light
- Each beam can pass one splitter, not two. A splitter halves a beam. A target still counts half-strength light, but a quarter is too faint. So the beam reaching a target can't have passed through two splitters. That rules out many routes.
- Wrong colours block a target. A target that catches a colour it doesn't need shows an × and stays dark. Sometimes a mirror's job is to send a spare beam into a wall.
- Linked pieces are one switch. Pieces ringed in the same colour and joined by a dashed line always turn together. Settle the link using whichever member is easiest to decide, then check that the others still work.
- Bolted pieces are fixed. Pieces on a square plate never turn, but they still reflect and split light. Treat them as part of the walls.
- Not every piece matters. Random boards include decoy mirrors the solution never uses. If no beam can reach a piece, leave it alone.
Mistakes to avoid
Turning pieces at random is the most common one. With only two positions each, it feels harmless, but it hides cause and effect. Make one turn, then follow every beam it changes. Another mistake is fixing one target and forgetting the others. A turn that lights one target can send a stray colour into another. Undo takes back any turn and lowers your count. Hint rings one piece that is worth turning.
A learning path
The twelve hand-made levels introduce one idea each, from a single mirror to walls, wrong colours, mixing, splitting, bolted pieces and links, ending with all three colours together. Play them in order, then move to the random boards. Easy is 6×6 with two colours. Medium is 7×7 and adds a splitter and linked pieces. Hard is 8×8 with all three colours. Aim for par on each.
