3 ms·

See Lights Out: https://en.wikipedia.org/wiki/Lights_Out_(game) https://en.wikipedia.org/wiki/Lights_Out_(game)

johnsondavies 5y ago
Thank you for putting my 16 LEDs Puzzle on Hacker News! Yes, the principle is similar to Lights Out, but in my puzzle pressing a button toggles its LED and all the other LEDs on the same diagonal(s). I found that this rule is harder to solve, even on a 4x4 grid.
- tromp 5y ago
  Using diagonals decomposes the puzzle into 2 disjoint puzzles according to the black and white squares in a checkerboard pattern. One puzzle can be marked as _ A _ B C _ D _ _ E _ F B _ G _ If we denote the corresponding buttons in lowercase, we have the equation A 1 0 1 1 0 1 0 a B 0 1 0 1 1 0 0 b C 1 0 1 0 1 0 1 c D = 1 1 0 1 1 1 0 d E 0 1 1 1 1 0 1 e F 1 0 0 1 0 1 1 f G 0 0 1 0 1 1 1 g Where A=1 if and only if light A needs to change. This matrix over GF(2) is not invertible; its rank is only 5, so the lights cannot be changed arbitrarily. By Gaussian elimination, one finds that button f does the same as buttons a b e together, and button g the same as b c d together. This reduces the equation to A 0 1 1 1 1 a B 0 1 0 1 1 b C = 1 1 0 1 1 c D 0 0 0 1 0 d E 0 0 0 0 1 e and the solution comes out as e = E d = D c = A B b = B D E a = B C Solving for the remaining buttons yields e = E d = D c = A B b = B D E a = B C
  - tromp 5y ago
    Oops; I can't edit my post anymore. It went south starting from > This reduces the equation to We instead just ignore buttons f and g, and invert the equation A 1 0 1 1 0 a B 0 1 0 1 1 b C = 1 0 1 0 1 c D 1 1 0 1 1 d E 0 1 1 1 1 e to a 0 1 0 1 0 A b 1 1 1 0 0 B c = 0 1 0 0 1 C d 1 0 0 1 1 D e 0 0 1 1 1 E Showing which buttons to press in terms of exclusive-or of wrong lights, e.g. press button a if exactly one of lights B and D is wrong.
MarkusWandel 5y ago
Here's a video of the cube version: https://www.youtube.com/watch?v=CUUoLWqZhdk https://www.youtube.com/watch?v=CUUoLWqZhdk They seem to be rare. I have one from a garage sale, years ago. Maybe I should check that the batteries in it haven't leaked, and not let the kids destroy it.

Thank you for putting my 16 LEDs Puzzle on Hacker News! Yes, the principle is similar to Lights Out, but in my puzzle pressing a button toggles its LED and all the other LEDs on the same diagonal(s). I found that this rule is harder to solve, even on a 4x4 grid.

tromp 5y ago
Using diagonals decomposes the puzzle into 2 disjoint puzzles according to the black and white squares in a checkerboard pattern. One puzzle can be marked as _ A _ B C _ D _ _ E _ F B _ G _ If we denote the corresponding buttons in lowercase, we have the equation A 1 0 1 1 0 1 0 a B 0 1 0 1 1 0 0 b C 1 0 1 0 1 0 1 c D = 1 1 0 1 1 1 0 d E 0 1 1 1 1 0 1 e F 1 0 0 1 0 1 1 f G 0 0 1 0 1 1 1 g Where A=1 if and only if light A needs to change. This matrix over GF(2) is not invertible; its rank is only 5, so the lights cannot be changed arbitrarily. By Gaussian elimination, one finds that button f does the same as buttons a b e together, and button g the same as b c d together. This reduces the equation to A 0 1 1 1 1 a B 0 1 0 1 1 b C = 1 1 0 1 1 c D 0 0 0 1 0 d E 0 0 0 0 1 e and the solution comes out as e = E d = D c = A B b = B D E a = B C Solving for the remaining buttons yields e = E d = D c = A B b = B D E a = B C
- tromp 5y ago
  Oops; I can't edit my post anymore. It went south starting from > This reduces the equation to We instead just ignore buttons f and g, and invert the equation A 1 0 1 1 0 a B 0 1 0 1 1 b C = 1 0 1 0 1 c D 1 1 0 1 1 d E 0 1 1 1 1 e to a 0 1 0 1 0 A b 1 1 1 0 0 B c = 0 1 0 0 1 C d 1 0 0 1 1 D e 0 0 1 1 1 E Showing which buttons to press in terms of exclusive-or of wrong lights, e.g. press button a if exactly one of lights B and D is wrong.

MarkusWandel 5y ago

Here's a video of the cube version: https://www.youtube.com/watch?v=CUUoLWqZhdk https://www.youtube.com/watch?v=CUUoLWqZhdk They seem to be rare. I have one from a garage sale, years ago. Maybe I should check that the batteries in it haven't leaked, and not let the kids destroy it.