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48 votes
Accepted

Is there any easy way to solve this lock puzzle?

There is an easy way to solve it in the minimum number of moves. The reason this works is:
Jaap Scherphuis's user avatar
19 votes

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

To test if a 5x5 Lights Out pattern is solvable, you need to check two things. First look at the top, middle and bottom rows, at the first two and last two lights - the 12 lights bolded here: [1, 0, ...
Jaap Scherphuis's user avatar
17 votes

Is there any easy way to solve this lock puzzle?

I don't know why this works, but I tried my old strategy from other similar puzzles and it has worked in several cases so far: Then, One final note - since I don't know why it works, I also can't ...
hdsdv's user avatar
  • 5,190
16 votes

Will you be the first to get free?

There is a simple solution. Because
Florian F's user avatar
  • 30.6k
16 votes
Accepted

Board with all 2020s

It is Reasoning:
WhatsUp's user avatar
  • 7,407
16 votes

Prime lights out

Via integer linear programming, the minimum number of moves turns out to be: This same solution minimizes the largest prime. By request, here's the SAS code I used: ...
RobPratt's user avatar
  • 14k
15 votes
Accepted

Prime lights out

Here is my solution: How I found this:
Jaap Scherphuis's user avatar
14 votes
Accepted

Counter Flipping

Edit: Now that I have a bit more time, and my answer is already the accepted one, I'll add a short summary of the theory of this type of game which most of the other answers have touched on. This is ...
Jaap Scherphuis's user avatar
13 votes
Accepted

Lights out game on a chessboard

The winner is The winning strategy To see this,
xnor's user avatar
  • 27.3k
13 votes

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

Suppose there are $n\geq 3$ chips. It's easy to see that $n$ moves is possible, making each move exactly once (this flips each chip three times). Since making the same move twice cancels out, any ...
Especially Lime's user avatar
12 votes

Is there any easy way to solve this lock puzzle?

Or, create a new blank board, and click on it all the positions of the 'on' switches from the original board. Take this new pattern back to the original board, and click every 'off' position from the ...
JMP's user avatar
  • 35.6k
12 votes
Accepted

Flipping coins in a circle

tehtmi's user avatar
  • 3,326
10 votes

Prime lights out

Here is my solution without doing any computation.
WhatsUp's user avatar
  • 7,407
10 votes

Flip counters in a grid so that they alternate in color

I am not sure if this is optimum but I can do it in six moves:
PDT's user avatar
  • 15.5k
8 votes

Is a game of Knight's out possible?

The first variant of Knights Out is solvable. In fact, given any network of lights where toggling a light also toggles its neighbors, it is possible to turn on all the lights! This beautiful fact ...
Mike Earnest's user avatar
  • 32.5k
8 votes

Board with all 2020s

A less technical solution: We can (try to) make a symmetric solution that makes all numbers equal (where the 6 variables signify how often a cell is chosen): ...
Retudin's user avatar
  • 81
8 votes
Accepted

Minimum number of flips needed to fully set a binary string

Find a good invariant You need to see if if you can work towards the solution To find the number of flips needed:
Retudin's user avatar
  • 9,218
8 votes

Minimum number of flips needed to fully set a binary string

This is a refinement of @Retudin's very nice invariant which makes it easy to calculate the required number of flips in linear time: Given a binary string, for example, ...
loopy walt's user avatar
  • 21.3k
8 votes
Accepted

Flip counters in a grid so that they alternate in color

A simple proof that PDT's solution is optimal:
Bubbler's user avatar
  • 15.4k
7 votes
Accepted

Is a game of Knight's out possible?

Every Lights Out game where the lights have two states (on/off) which is reflexive (the pushed light also toggles) and which is symmetric (if light A is a neighbour of B, then B is a neighbour of A)...
Jaap Scherphuis's user avatar
7 votes
Accepted

Will you be the first to get free?

Yes. Explicit Grid
Display name's user avatar
  • 2,260
7 votes
Accepted

Different numbers in all cells of a 3x3 board

Make these presses: To get these values: You can solve the problem via integer linear programming as follows. Let nonnegative integer decision variable $x_{i,j}$ be the number of times that cell $(...
RobPratt's user avatar
  • 14k
7 votes
Accepted

The combinational switching lights

You need First, an important thing to know: If S≤L: If S≥L: Time for some math! The setup: The Important Thing: So, what does this tell us?
Deusovi's user avatar
  • 147k
7 votes
Accepted

Deemo II Candle Puzzle

This puzzle is a version of lights-out. There is a large amount of theory behind these games, but this is quite a simple variant. Two observations help enormously: Doing a move twice has no effect. ...
Jaap Scherphuis's user avatar
6 votes
Accepted

Maximising the number of lit lightbulbs through row-column toggling

The answer is Reasoning for even $n$: Reasoning for odd $n$:
Reinier's user avatar
  • 5,167
6 votes

Prime lights out

daw's user avatar
  • 3,208
6 votes

Flip counters in a grid so that they alternate in color

Label the rows by A, B, C, D from top to bottom, and columns by 1, 2, 3, 4 from left to right. This is minimal because Also,
mathmandan's user avatar
  • 1,053
5 votes
Accepted

I am struggling with a complex version of the "lights out" puzzle

You are basically trying to solve a linear algebra question, but with XOR instead of addition. The good news is that this can be done in the usual way. See this math.SE article. So, let me back up. ...
Dr Xorile's user avatar
  • 23.7k
5 votes

Will you be the first to get free?

Adding some findings to the answer by Display name. As already noted, Call the coin positions 1 2 3 4 5 6 7 8 9 and label the guard's moves with digits for the ...
aschepler's user avatar
  • 1,485

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