# Tag Info

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:
• 53.7k

### 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, ...
• 53.7k

### 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 ...
• 5,190

### Will you be the first to get free?

There is a simple solution. Because
• 30.6k
Accepted

It is Reasoning:
• 7,407

### 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: ...
• 14k
Accepted

### Prime lights out

Here is my solution: How I found this:
• 53.7k
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 ...
• 53.7k
Accepted

### Lights out game on a chessboard

The winner is The winning strategy To see this,
• 27.3k

### 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 ...
• 2,943

### 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 ...
• 35.6k
Accepted

• 3,326

### Prime lights out

Here is my solution without doing any computation.
• 7,407

### 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:
• 15.5k

### 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 ...
• 32.5k

### 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): ...
• 81
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:
• 9,218

### 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, ...
• 21.3k
Accepted

### Flip counters in a grid so that they alternate in color

A simple proof that PDT's solution is optimal:
• 15.4k
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)...
• 53.7k
Accepted

### Will you be the first to get free?

Yes. Explicit Grid
• 2,260
Accepted

• 5,167

• 3,208

### 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,
• 1,053
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. ...
• 23.7k