About

Description of Lights Out 2000: This version is very similar to the classic version, i.e. a 5×5 grid of buttons with lights which you have to switch off in as few moves as possible. The difference lies in the fact that now the lights are not just on or off, but have 3 states - off, red, or green. When a button is pressed the same lights change as before, but now they go from off to red to green and then off again. If you buy only one Lights-Out game, I would recommend this one, because not only does it do this 3-state puzzle, it also incorporates the classic Lights Out puzzle, and has an action game and a 2 player game as well. For a short time in 2001 this version was sold without the 2000 tag, but now Tiger has re-released the original classic Lights-Out in a new design that looks very similar to the Lights-Out 2000. The Lights-Out 2000 can be easily recognised by the obvious tiger-paw arrangement of the buttons. The mathematics of the 3-state puzzle is much the same. The move order is unimportant, and pressing a button three times has no effect, so no button has to be pressed more than twice to solve any position. All the mathematics works the same way, except that the arithmetic is done modulo 3 instead of modulo 2. Quiet patterns: This puzzle has five types of quiet patterns: (grey means press once, black twice) 1 . . . 2 2 2 . 1 1 1 2 . 1 2 1 1 . 2 2 . 2 . 1 . 1 . 1 . . 2 1 2 2 . 2 1 . 2 1 1 2 1 1 . 1 1 2 2 1 . 1 2 2 2 2 . 1 . 2 1 2 . 1 2 1 . 2 . 1 1 1 1 2 . 1 . 2 . 1 2 . 1 . 2 . . . . . 1 . 2 . 1 2 . 1 . 2 1 1 . 2 2 1 1 . 2 2 . . . . . 2 2 . 1 1 2 2 . 1 1 These patterns can occur in any orientation, in mirror image, or with the colours swapped. Together with the trivial quiet pattern (no buttons pressed at all) this leads to 27=33 quiet patterns. This suggests that this time there are three buttons that need never be used. The number of positions: Three buttons need never be used to solve the puzzle, so 22 buttons are enough. Each button can be pressed up to two times, giving a total of 322 = 31,381,059,609 positions for the lights. The built-in puzzles need between 5 and 24 moves to solve, and this seems to imply that any position can be solved in at most 24 moves. I have now verified this by calculating the number of possible positions for each number of buttons pressed. The results can be seen on the tables page. Solution to Lights Out 2000: For each light on row 1, press the button beneath it on row 2 once or twice to turn the light off. This way row 1 is completely unlit. Repeat step a for rows 2-4, so that now you only have lights on row 5. This is usually called 'chasing the lights'. If the light at A5 is red then press B1 twice, if it is green press it once. If the light at B5 is red then press A1 and B1 twice, if it is green press them once. Repeat steps a-b, chasing the lights down and it will be magically solved. To get a minimal solution, the same method can be used as for the classic version, except that there are now 26 quiet positions to check. The built-in puzzle problems can be solved using the above method, or you can simply look up the solution on this page, which also includes the solutions to the built-in puzzles of the classic game. If your browser has JavaScript, then you can play the Lights Out 2000 game: