THE CORE RULE
Adjacent cells on the path must hold consecutive numbers. Cell N must be directly next to cell N−1 and cell N+1. "Adjacent" in a Circular Maze means sharing an edge in the ring topology — inward one ring, outward one ring, or one step clockwise or counter-clockwise within the same ring.
The path visits every cell exactly once and forms a single chain from the smallest to the largest number. The solution is unique — deduction, not search.
THE TOPOLOGY: RINGS ARE NOT ROWS
Unlike a rectangular grid, rings wrap around: the first and last cell in a ring are adjacent. The innermost ring has no inward neighbour — every cell there is accessible only from within the ring itself or from the next ring out. The outermost ring has no outward neighbour.
This asymmetry has a direct consequence: the innermost ring is the most constrained area. Any path segment that enters the inner ring must exit the inner ring, and the small number of cells in that ring limits how many routes are available. The outer rings are looser — more cells, more choices — which is why you should solve inner-out, not outer-in.
GAPS BETWEEN CLUES ARE YOUR UNITS OF WORK
Between two consecutive clue cells, the path must pass through a fixed number of intermediate cells — the gap. A gap of 1 between two clues means exactly one cell lies between them in the sequence, and that cell must be a common neighbour of both clue positions.
Sort all gaps smallest-first. Small gaps near the inner ring are especially productive because the inner topology limits routing choices sharply.
A gap of 0 means the two clues must be adjacent. Confirm adjacency first — it's the cheapest forced move in the puzzle.
DEAD-ENDS AND RING-BOUNDARY FORCING
A dead-end cell has only one free neighbour. A middle-of-path cell in that state forces the neighbour to hold either its predecessor or successor. Scan for dead-ends after every placement.
Ring boundaries — cells where the path must cross from one ring to another — are a special case. A cell at a ring boundary has two possible cross-ring neighbours (one inward, one outward) plus two within-ring neighbours. As nearby cells fill, the cross-ring neighbour count often drops to one, forcing the crossing direction.
CONNECTIVITY CHECK
As you place cells, confirm that all remaining empty cells are still reachable from both the current path head and tail. A group of cells cut off from the rest by filled cells — with only a single entry point — forces the path through that entry in a specific direction.
In Circular Maze, isolated pockets often form when the path wraps around the inner ring and unintentionally blocks a ring segment behind it. Check both the inner region and the outer region after placing any inner-boundary cell.
THE SOLVING LOOP
- Orient yourself: count cells per ring, identify innermost-ring size.
- List all gaps. Note which gaps span ring boundaries or involve inner-ring cells.
- Force gap-0 adjacencies. Then force any gap-1 segments via shared neighbours.
- Examine inner-ring clues — their limited routing forces segments cheaply.
- Cascade dead-ends after every placement.
- Verify connectivity; prune candidates that isolate pockets.
- Repeat until solved.
THE BEGINNER MISTAKE
Tracing from cell 1 outward, choosing ring direction by feel. Ring wrap-around makes forward-tracing especially disorienting — routes look blocked and then suddenly re-open. Instead, anchor from clue cells inward, work the inner ring first, and let forced moves propagate outward. The inner topology resolves faster than it looks.