How to Solve Arrow Maze Puzzles

Arrow Maze, sometimes called Arrow Path, requires you to find the correct path through the arrows by writing down the numbers from 1 to X, where X is the highest possible number in the grid. In our 5×5 example, that would be 1-25. In a 5×9 puzzle, you would be using the numbers from 1-45.

The numbers you place will show the path through the arrows, in order.
Numbers already given tell you where that arrow is in the sequence.
Each arrow points toward the next one in the sequence.
The next arrow is not necessarily directly adjacent.
All cells will be used exactly one time each.

Arrow mazes are usually solved a piece at a time, from multiple points in the sequence. As you fill in numbers that you are certain of, others will become obvious.

In this case, let’s start with the first arrow. Arrow number 1 points to these two cells. Because one of them already has a number, number 14, we know that it cannot be arrow number 2. Therefore, The arrow pointing up must be arrow 2.

Also, arrow 15 only points toward a single cell, so that must be arrow number 16.

Sometimes, you will look in more than one direction to figure out the number to use.

Here, arrow 16 points to all of the green cells. To figure out which one is arrow 17, we must use additional information.

As you can see, only the blue arrow also points toward arrow 18, so it must be arrow number 17.

You can also figure out numbers by looking backward in the sequence.

Because we marked arrow number 17, there is now only one arrow left in the grid that points toward arrow number 23.

That means that the green arrow must be number 22.

We can do that again. This is the last arrow pointing at number 22, so it has to be arrow 21.

And again. For the same reason, this is arrow 20.

One more time, and the green arrow must be number 19. As you can see, arrow 18 points toward it.

At this point, we have determined arrows 1 and 2, and then the sequence from 13 through 25. That means we need to determine arrows 3 through 12 to complete the grid.

With many logic puzzles, it is common to reach a point of trial and error. Here, we have two possible arrows pointing toward 13 that could be number 12. Arrow number 2 points toward three unlabeled arrows.

Because there are fewer possibilities, we will try to solve backward from 13 until we reach an arrow we cannot point toward. Let’s try the red arrow first. I will leave it red as we test so we know where our starting point was.

Both the green and blue arrows point toward our tentative number 12. Let’s try blue first.

Solving backward, we quickly find arrow 10, and then arrow 9. However, there is now no arrow that is left to point toward our tentative arrow number 9, so this blue sequence is not the correct one.

Now we can check the green path.

There is only a single arrow pointing toward our test arrow 11. Looking directly above it, you would at first think we’d be splitting into a couple more branches to continue checking backward.

However, by filling in that 11, it leaves only one more arrow for the 2 to point at. Following the blue path, we get to arrow number 4, which then points at our arrow number 10, declaring it to instead be arrow number 5.

Since it can’t be both, this entire branch is incorrect. This was the only other option for our red arrow 12, which means that the arrow immediately below the 13 must be the correct number 12.

Now that we know for certain where arrow 12 is, we can continue our backward sequence. This is the only arrow pointing toward 12, so it must be number 11.

Again, this is the only arrow pointing toward number 11, so it must be arrow number 10.

And this green arrow must be number 9, because the only other arrows pointing in the direction of number 10 are arrows 2, 18, and 17. Obviously, it can’t be any of them.

Just for fun, we’re going to shift direction and look forward from arrow number 2. Remember the blue path of arrows that caused our conflict earlier?

Because we now know for certain that the green arrow is number 9, this sequence caannot be correct. That leaves only one other arrow that number 2 is pointing toward, so we know it is arrow number 3.