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Questions tagged [lights-out]

A type of puzzle typically involving a grid of lights, in which the challenge is to get them all to the same state (on or off). The trick is that each light also affects a number of its neighbors, with sides and corners affecting fewer.

24 votes
3 answers
4k views

Is there any easy way to solve this lock puzzle?

https://js13kgames.com/games/lock-puzzle/index.html The link provides an online puzzle game of $16$ tiles in the form of a $4 \times 4$ matrix of which some entries are in the form of vertical tiles ...
math maniac.'s user avatar
18 votes
5 answers
1k views

Board with all 2020s

Zeroes are written in all cells of a $5 \times 5$ board. We can take an arbitrary cell and increase by 1 the number in this cell and all cells having a common side with it. Is it possible to obtain ...
nonuser's user avatar
  • 890
12 votes
4 answers
2k views

Prime lights out

You start with a 4x4 grid filled with zeroes. If you press a cell then the cell and all its neighboring (horizontally and vertically) cells will have their numbers increased by 1. What is the most ...
Dmitry Kamenetsky's user avatar
11 votes
1 answer
556 views

Lights out game on a chessboard

Alice and Bob play a game with an 8×8 grid of lights, all initially on. They take turns choosing a light which is on and turning it off, with Alice going first. However, the grid is rigged such that ...
Mike Earnest's user avatar
  • 32.5k
11 votes
2 answers
952 views

Turn on all squares

Take a square grid of size $a\times b$, with all squares being off. You can tap a square, to reverse the state of that square and all squares located in the same column and row as the tapped square. ...
Vepir's user avatar
  • 2,968
10 votes
1 answer
1k views

How do I determine whether a 5x5 Lights-Out puzzle is solvable without trying to solve it?

The following two 5x5 Lights-Out puzzles are not solvable. Is there a way to find out why, without trying to solve them? [1, 0, 0, 1, 0] [1, 1, 1, 1, 0] [1, 1, 1, 0, 0] [0, 0, 1, 0, 0] [1, ...
Apostolos's user avatar
  • 201
9 votes
3 answers
940 views

Minimum number of flips needed to fully set a binary string

Source: My school teacher, it was just given as a problem statement. Problem: You are given a binary sequence $S$ of up to $10^6$ bits. You wish to set all the bits in the string to $1$, but the catch ...
user88178's user avatar
  • 103
9 votes
2 answers
317 views

Christmas light horror story!

Inspired by stories of strangely behaved Christmas lights here on Puzzling, I feel comfortable now to share my own Christmas light horror story. It all started when I ordered a grid of star lights on ...
TheGreatEscaper's user avatar
9 votes
1 answer
313 views

Putting up the lights

Feeling festive, you decide it's time to put up the lights. You dig out the box and plug a strand in. Uh oh, they are all the same color. This won't work, these are supposed to be multiple colors ...
David Starkey's user avatar
7 votes
6 answers
1k views

Counter Flipping

A counter flip game is played in the following way: In each move, you can flip an entire row or column Flipping a row or column inverts all the counters on that row or column from $X$ to $O$ or vice ...
Noah P's user avatar
  • 170
7 votes
1 answer
1k views

Name and solution of puzzle to rotate all arrows to same direction

In this puzzle, when you click an arrow, all arrows immediately next to it (diagonally included), as well as the arrow you clicked itself rotate 90 degrees. The goal is to get all the of arrows to ...
Samuel's user avatar
  • 71
6 votes
4 answers
904 views

Flip counters in a grid so that they alternate in color

Beginner puzzle This puzzle is intended to be suitable for people who are new to puzzle solving. Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle. ...
Will.Octagon.Gibson's user avatar
6 votes
4 answers
464 views

How to get the least number of flips to a plastic chips to get a certain figure?

The puzzle is as follows: (Transcription with grammar errors fixed) A game consists of the following: The challenge is to flip the chips in such a way so that they are as in state 2. You start in ...
Chris Steinbeck Bell's user avatar
6 votes
3 answers
398 views

Different numbers in all cells of a 4x4 board

This is a harder version of this puzzle: Different numbers in all cells of a 3x3 board Zeroes are written in all cells of a 4×4 board. Pressing a cell increases by 1 the number in this cell and all ...
Dmitry Kamenetsky's user avatar
6 votes
3 answers
1k views

Flipping coins in a circle

We have a set of N coins that are all placed in a circle. They all have "Tails" as their face up side. The coins are all distinct and have numbers (1,2,3...N) written on them. In each move, ...
Hemant Agarwal's user avatar

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