THE SHORT VERSION
Number Mazes: place 1 to N on a square grid so the numbers form a connected path. Each consecutive pair (k, k+1) must occupy orthogonally adjacent cells — only up, down, left, right. Every cell is visited exactly once.
Starlink: same rule, but consecutive numbers may occupy any of the eight neighbouring cells — orthogonal or diagonal. The path visits every cell exactly once; the movement options are wider.
Same sequential constraint. Different neighbour count. Harder to force placements.
SIDE BY SIDE
Movement
Number Mazes: orthogonal only (N/S/E/W)
Starlink: orthogonal + diagonal (8 directions)
Interior cell neighbours
Number Mazes: 4
Starlink: 8
Corner cell neighbours
Number Mazes: 2 (maximum forcing power)
Starlink: 3 (less forcing power)
Edge cell neighbours
Number Mazes: 3
Starlink: 5
Valid paths per gap
Number Mazes: fewer
Starlink: many more
Relative difficulty at same gap count
Number Mazes: easier
Starlink: harder
WHAT STAYS THE SAME
The core technique is identical: compute the gap between each pair of consecutive given clues (gap = higher clue − lower clue − 1), then work from the smallest gaps first. A gap of 0 means adjacent clues must occupy neighbouring cells — the most direct forcing situation.
Dead-end analysis transfers. Any cell that has only one valid neighbour the path can enter from must be visited from that direction. Any cell that can only be reached from one other unclaimed cell is forced regardless of which gap it belongs to.
Connectivity pruning works in both variants. A candidate path segment that would cut the remaining unvisited cells into an isolated pocket is always illegal — the path must be able to reach every cell. This check has nothing to do with the number of neighbours per cell; it is purely about reachability.
HOW DIAGONALS CHANGE STRATEGY
In Number Mazes, a gap-1 pair (one unknown cell between two given clues) means that missing cell must be a shared orthogonal neighbour of both clues. With only 4 neighbours each, the intersection is small — often just one or two candidates.
In Starlink, that same gap-1 pair has 8 neighbours per clue cell. The intersection is much larger; multiple cells may qualify. You cannot resolve many gap-1 positions by neighbourhood intersection alone. Instead, you must combine it with connectivity pruning: of the candidate cells, which ones would create an isolated pocket if placed? Eliminating those candidates is the primary tool.
Corner cells illustrate the difference starkly. A Number Maze corner has 2 neighbours — the path enters one and exits the other, fully determined. A Starlink corner has 3 neighbours. Entering from either of two directions still leaves ambiguity. Corners stop being free placements and become genuine decision points.
WHICH IS HARDER?
Starlink is consistently harder at the same gap count and grid size. The higher branching factor means fewer forced placements per pass, more connectivity pruning required before candidates collapse, and more frequent need to explicitly track which paths would and would not connect the remaining cells.
As a rough calibration: a Starlink easy level is comparable in effort to a Number Maze medium. The same gap count produces a much harder puzzle because the diagonal options multiply the candidate paths at every step.
WHEN TO MAKE THE SWITCH
If you play Number Mazes: try Starlink when medium Number Mazes feel automatic — when you can work through gaps without writing candidates down. Your gap-logic and connectivity instincts carry over fully. The challenge is adjusting to a higher branching factor rather than learning new rules.
If you play Starlink: try Number Mazes when you want a faster resolution rhythm. The lower branching factor means more cells fall into place without explicit enumeration, and corner forcing gives you free placements that Starlink rarely offers. A good session warm-up.
Playing both sharpens different aspects of path reasoning. Number Mazes trains the instinct for when a cell is truly forced by structure alone. Starlink trains explicit connectivity tracking and the discipline of eliminating disconnecting moves before committing.