Eshai Wuuen
New member
- Joined
- Jun 19, 2020
- Messages
- 1
I'm not sure if this is the right thread to post this question, but it seemed right.
This is a question that popped into my head while playing a logic puzzle which requires you to make a single unbroken loop within a grid of dots. Though while playing, I began to wonder something:
If given a grid of x and y dots, is there a mathematical formula of some sort to find how many unique single unbroken loops can be made within the grid?
Some things I realized on my own:
* The grid of dots in the game can be arranged in many ways to form shapes other than squares, although a square (or rectangular) grid is what I'm trying to focus on.
* Not all the dots on the grid have to be used, so a 1x1 square on a 5x5 grid is valid.
* Sliding, rotating, mirroring ect. the shape within the grid are considered different and unique solutions, so a 1x1 square would have 25 unique places on a 5x5 grid.
* As a reminder, the shape doesn't have to be square. As long as as the line that creates it is a single unbroken loop, it counts.
*Only one shape per solution.
I really have no idea where to start with this one. There seem to be so many different variables to factor in. I hope I provided enough information to help me get started.
(The two images I included show examples from the game. The first is the square grid, which is the base of my question. No diagonal lines allowed, as shown. The second image shows a different alignment of dots that can form triangles instead. Not what I'm looking for.
Thank you!
-Tyler
This is a question that popped into my head while playing a logic puzzle which requires you to make a single unbroken loop within a grid of dots. Though while playing, I began to wonder something:
If given a grid of x and y dots, is there a mathematical formula of some sort to find how many unique single unbroken loops can be made within the grid?
Some things I realized on my own:
* The grid of dots in the game can be arranged in many ways to form shapes other than squares, although a square (or rectangular) grid is what I'm trying to focus on.
* Not all the dots on the grid have to be used, so a 1x1 square on a 5x5 grid is valid.
* Sliding, rotating, mirroring ect. the shape within the grid are considered different and unique solutions, so a 1x1 square would have 25 unique places on a 5x5 grid.
* As a reminder, the shape doesn't have to be square. As long as as the line that creates it is a single unbroken loop, it counts.
*Only one shape per solution.
I really have no idea where to start with this one. There seem to be so many different variables to factor in. I hope I provided enough information to help me get started.
(The two images I included show examples from the game. The first is the square grid, which is the base of my question. No diagonal lines allowed, as shown. The second image shows a different alignment of dots that can form triangles instead. Not what I'm looking for.
Thank you!
-Tyler