Lamp Switch

Lamp Switch is a puzzle about cause and effect. Each press changes a small cross of lamps at once, and you have to work out which lamps to press so that the whole board goes dark.

How to play

The goal is to turn every lamp off.

• Pressing: tap a lamp. It switches, and so do the lamps directly above, below, to the left and to the right of it. A lamp at an edge or a corner has fewer neighbors, so it changes fewer lamps.
• Reading the board: a lit lamp glows yellow with a bright center. A dark lamp is a gray ring.
• Counting presses: the page shows how many presses you have used. It also shows the fewest presses that can solve the board, so you know how close you are to a perfect solution.
• Winning: the moment every lamp is dark, you win.

Undo takes a press back and costs nothing, and Restart sets the board up again as it began. The Hint button lights up a lamp that belongs to the shortest way out. It is available on Easy, Medium and Hard, and not on Expert.

Every board is made by starting with all lamps dark and pressing random lamps. That means a solution always exists. It also means you can solve any board by working backwards: the lamps that were pressed to make it are the lamps to press again.

On a phone, tap the lamps with your finger. On a computer, click them with the mouse. The lamps are large, so they are easy to hit.

The levels

The levels change the size of the board and how many presses the best solution needs.

• Easy: a small 4 by 4 board. The shortest solution takes three to five presses.
• Medium: a 5 by 5 board. The shortest solution takes six to nine presses.
• Hard: a 5 by 5 board that is tangled. The shortest solution takes ten presses or more.
• Expert: a 6 by 6 board whose shortest solution takes twelve presses or more. You may use at most the shortest number plus two, and you get no hints.

The fewest-presses figure is worked out with a method from linear algebra that treats each lamp as one equation, so the number you see is exact.

Today's game

The daily game is a Medium board. Everyone who plays on the same calendar day gets the same pattern of lit lamps.

Tips

1. Pressing the same lamp twice does nothing, because the second press undoes the first. So never press a lamp twice. Think of each lamp as pressed or not pressed.
2. The order of your presses does not matter. Only which lamps you pressed counts, so you can do them in any order you like.
3. Work from the top row down. To switch off a lit lamp without disturbing the rows above, press the lamp directly beneath it.
4. Use Undo to test a press. If it lights more lamps than it clears and you cannot see a use for it, take it back.
5. Learn the feel of it on a small board first. The 4 by 4 Easy board shows quickly how a single press spreads.
6. Watch the counter against the fewest presses. If you are well over, you have probably pressed a lamp twice somewhere.
7. On Expert, plan before you press. You only have two spare presses.

Questions

Can every board be solved? Yes. Each board is made from a dark board by pressing lamps, so the same presses, repeated, will turn it off again.

What is the "fewest" number? It is the smallest number of presses that can turn every lamp off. You can finish with more, but never with fewer.

Why is there no Hint on Expert? Expert is meant to be a real test. It also has a limit of the fewest presses plus two.

Does the order of presses matter? No. Pressing A and then B gives the same board as pressing B and then A.