# Can Arrows puzzles have multiple solutions?

I am trying to make an Arrows puzzle, but I don't know if there are multiple solutions.

For those who don't know, an Arrows puzzle starts with a grid of numbers (example from SE) surrounded by empty boxes.

The goal is to put an arrow into each outer box such that the number in each square in the grid matches the number of arrows pointing at it. Arrows must either be pointed directly at the grid or at a 45 degree diagonal.

The solution for that puzzle is therefore (credit to Sconibulus for the solve):

The question then is can an Arrows puzzle have multiple solutions?

• Welcome to the site! This question is a little bit unclear, as it stands - your image doesn't clearly indicate what an ArrowsPuzzle is, and you probably need to describe clearly the criteria of the puzzle before we can know whether it's possible to have multiple solutions or not. Jul 1 '21 at 9:33
• It appears that the objective is to arrange arrows on the border such that each cell is pointed at by its corresponding number of arrows. Jul 1 '21 at 11:43
• Relevant, possibly a duplicate (especially the second-voted answer): puzzling.stackexchange.com/q/2 Jul 1 '21 at 14:17

## 1 Answer

If my comment is correct, and an Arrows Puzzle is one in which you are given a grid of numbers and asked to arrange arrows around the border such that each cell is seen by [cell's number] arrows, then the following grid has at least two solutions:

Many more grids of similar construction exist.

• I agree that for any size grid, there is an arrow puzzle with more than one solution. I think it is interesting though that when the size of the grid is increased, the number of clues grows faster than the number of arrows to be found. So for larger grids it seems that a larger proportion of the arrow puzzles with a solution have a unique solution. Jul 1 '21 at 13:06
• I believe this as well, but I can't even imagine what an average deduction would look like so there's no way to be sure. Jul 1 '21 at 15:59