3
$\begingroup$

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.

enter image description here

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):

enter image description here

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

Improve this question
$\endgroup$
2
  • 2
    $\begingroup$ 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. $\endgroup$
    – Rand al'Thor
    Commented Jul 1, 2021 at 9:33
  • 1
    $\begingroup$ 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. $\endgroup$
    – AxiomaticSystem
    Commented Jul 1, 2021 at 11:43

1 Answer 1

Reset to default
3
$\begingroup$

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:

enter image description here

Many more grids of similar construction exist.

Improve this answer
$\endgroup$
2
  • 2
    $\begingroup$ 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. $\endgroup$
    – Jaap Scherphuis
    Commented Jul 1, 2021 at 13:06
  • $\begingroup$ 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. $\endgroup$
    – AxiomaticSystem
    Commented Jul 1, 2021 at 15:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.