Lights Out Keychain

A tiny version of Lights Out (pocket size I suppose) produced by Tiger. This is played on a 4x4 grid, however the edges wrap around, so it's actually played on a Torus. So if you press a button on the top row, it will affect the state of those on the bottom row. In this version, however, you don't actually press the buttons, since it's played on a small LCD screen. There are a couple of arrow buttons that move a cursor around the display - when the cursor reaches the position of the button you'd like to press, you press the "enter" button. This makes it a little awkward to play (especially as the buttons are *so* small), but it is still a good puzzle. The game can be played in 4 modes Mode 1: 32 increasingly difficult puzzles Mode 2: Randomly chosen puzzles Mode 3: LIT ONLY mode. In this mode there are 32 increasingly difficult puzzles to solve. The difference to mode 1 is that you are only allowed to press lit buttons. This makes it similar to Flip. Mode 4: Create your own puzzles

You can play my Javascript Lights Out keychain to have a go for yourself. At the moment, it does not playt the Lit Only game, but this is on the way...

Solving Lights Out Keychain

What follows is a method of solving any Lights Out Keychain puzzle, which is similar to the standard "Light chasing method for ordinary Lights Out (See here for a description of Light Chasing). This method is far from satisfactory, since it doesn't come close to giving you the shortest solution, and it does not generalise to larger Torii. If you can devise a better solution method please let me know.

The method is as follows :

Chase the lights down from the top as if you were playing standard lights out on a 4x4 grid. If the puzzle is not solved at this point, there will probably be some lights on on the bottom row, as well as some on the top row (which you switched on when you pressed the buttons on the bottom row). If there are any lights lit on the top row, repeat the light chasing.

If, however, there are no lights lit on the top row, you need to chase the lights on the bottom row by pressing buttons on the top row (remember, we're on a torus here!). Now repeat the method.

You may need to go through this process a few times, but it always works! Indeed, Richard Gault has proved this for me (Click here to see his proof).

As I said at the beginning, this method virtually always takes significantly more than the minimum number of moves! However, if you keep track of which buttons you have pressed, then you can easily determine the shortest solution. It will consist of pressing exactly those buttons that you press an odd number of times in running through the above algorithm.

Coming Up

• Anyone have any idea whether all the LIT ONLY puzzles are solvable?
• Links (there is a great page of torus puzzles!)
• Lists of the preset puzzles (and solutions as I find them...)