STEP 1 — UNDERSTAND THE TOPOLOGY
Each cell in a Circular Maze has up to four neighbours: the cell directly inward (toward the centre), the cell directly outward (toward the edge), and the two cells beside it in the same ring (clockwise and counter-clockwise). Cells in the innermost ring have no inward neighbour. Cells in the outermost ring have no outward neighbour.
The innermost ring has the fewest cells — often 4–8 — so every path segment that enters the inner ring is highly constrained. Start any solve by counting how many cells are in the innermost ring.
STEP 2 — SORT CLUES AND COMPUTE GAPS
List every given clue in ascending order. Gap = (higher clue − lower clue − 1). A gap of 0 means the two clues must be adjacent; gap of 1 means one intermediate cell sits between them.
Sort gaps smallest-first. Fill them in that order.
STEP 3 — EXPLOIT INNER-RING CONSTRAINTS FIRST
The innermost ring is the most constrained area of the grid. Any clue number that falls in the innermost ring has no inward neighbour — the path can only approach it from the ring itself or from the next ring out. If the innermost ring has, say, 6 cells, the path segment threading through it can only take a handful of routes.
Check whether any clue sits in the inner two rings. A small-gap pair spanning the inner ring boundary is often completely forced.
STEP 4 — FILL SMALL GAPS VIA SHARED NEIGHBOURS
For gap-1: the missing cell must be a common neighbour of both anchor cells. List the four neighbours of each anchor and find the intersection. If it contains a single cell, place it immediately.
For gap-2: enumerate the short routes between the anchors. Any cell that appears in every valid route is forced — place it even if the full route isn't yet determined.
Remember that "neighbour" in Circular Maze means inward, outward, clockwise, or counter-clockwise — not diagonal. The ring geometry can make shared-neighbour analysis slightly less obvious than on a rectangular grid, so it's worth sketching the ring positions when analysing a gap.
STEP 5 — CASCADE DEAD-ENDS AFTER EVERY PLACEMENT
After placing any number, scan surrounding cells for those with only one free neighbour remaining. A middle-of-path cell with one free neighbour is a dead-end: the one free neighbour must hold the predecessor or successor. Place it and continue cascading.
Dead-end cascades are the fastest technique in Circular Maze. One forced placement near an inner-ring boundary often propagates through an entire ring segment.
STEP 6 — CONNECTIVITY PRUNING
The path visits every cell exactly once. If a candidate segment would wall off a group of cells from the rest of the empty grid, that segment is illegal. Check connectivity after placing each segment — an isolated group with a single entry forces the path through that entry in a specific direction.
SOLVING ORDER
- Orient yourself — count cells per ring, note inner-ring size.
- Sort clues, compute all gaps.
- Examine inner-ring and inner-boundary clues first.
- Fill gap-0 adjacencies, then gap-1 via shared neighbours.
- After each placement, cascade dead-ends.
- Prune with connectivity checks.
- Move to the next smallest unfilled gap and repeat.
Most beginner Circular Mazes resolve from inner-ring forcing and a single pass of dead-end cascades. Outer rings then fill in quickly because the inner segments constrain which numbers can appear at each ring boundary.
BEGINNER TRAP — TREATING RINGS AS ROWS
The ring topology wraps around: the first and last cell of each ring are adjacent to each other (they share a clockwise-to-counter-clockwise edge). A path that looks like it "hits a wall" at the ring boundary can actually continue by wrapping to the other side. Always trace the full ring perimeter before ruling out a route.