How to Solve Circular Maze: Beginner Strategies Step by Step

To solve a circular maze, work from both ends and use what the structure tells you. Each LogikLand circular maze has exactly one path from the arrow to the dot, so the job is to find it without wandering. These five steps are checked on a real easy maze and on counts from 300 generated mazes at each level.

Two ways to attack the maze

You can go forward from the entrance, or backward from the center. Beginners go forward and get lost in the outer rings, where the corridors are longest. Starting at the center is usually quicker, because there are few ways in. The maze below is the example for the whole page.

Step 1: start from the center

Look at the dot. Between the dot and the first ring there are six small cells. In the maze above, three of the six walls around the dot have a gap. In 300 easy mazes the dot had one opening 25 times, two openings 251 times and three openings 24 times, and the counts for expert mazes are 26, 258 and 16. So you will usually have to test two or three openings.

Follow each opening until it ends. In this maze two of the three lead nowhere: one pocket has only 1 cell and another has 6 cells, and both are closed. The third, which leaves the dot toward the left, leads into a region of 179 cells that contains the entrance. In a few seconds you have removed two wrong branches.

It does not always go so fast. In another easy maze we generated, the dot had two openings and the wrong one led into 94 cells, almost half of the maze, while the right one led into 92 cells. When both branches are big, follow the route from the entrance too, as in step 5.

Step 2: close the dead ends

A dead end is a cell with one open side only. This maze has 22. Mark each dead end with a small cross or a dot when you meet it, and never come back. Averaged over 300 mazes, an easy maze has about 21 dead ends and an expert maze about 118, so the more rings, the more you gain by marking them.

Step 3: accept the outward moves

The solution is not a steady march toward the middle. In this maze 9 of the 57 moves on the path go outward, away from the center. In all 300 generated mazes of each level the path had at least one outward move, and the share stays close to one move in five:

The path of the maze above shows it clearly. Counting the rings from the dot (ring 0) to the outer ring (ring 7), the path is already on ring 3 at its 14th cell. It then goes back out to ring 7, where it spends 14 more cells, and only gets inside ring 2 at the 55th of its 58 cells. A solver who followed the first inward corridor would have felt close to the middle, and been far from the answer.

So if you reach a corridor that goes outward, do not treat it as wrong. It may be the only way to a gap that lets you in again further along.

Step 4: scan the inner rings

The solution must cross every ring, and the rings near the center have few openings. Between the dot and the first ring there are 2 openings on average, between the first and second ring 4.9, and between the second and third ring 9.8, out of 6, 12 and 24 places where a gap could be. These are averages over the easy mazes, and the other levels give nearly the same numbers. Look at these small circles first: a gap you find there is one of very few, and the route must pass through one of them.

Step 5: meet in the middle

Use a pencil in one color from the dot outward, and a pencil in another color from the arrow inward. The two traces meet on the one path. Because the maze has no loops, once your two lines touch the problem is solved: the route is the entrance trace plus the center trace.

Mistakes to avoid

• Following an arc all the way round without looking for gaps in it. A gap in an arc is the way to the next ring.
• Missing a gap in a spoke, the short line that runs along a radius. It is the opening for moving around the ring.
• Starting with the long outer rings. They have the most cells and the longest corridors.

For the rules see circular maze rules, and for mazes with 16 or 20 rings, the methods in advanced circular maze techniques. The Circular Mazes assistant is reached from a free account. For ordinary square mazes, try the free sample generator on the maze book generator page.

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