DIAGONALS ARE REAL NEIGHBOURS
Unlike Sudoku or square mazes, Starlink counts diagonal cells as adjacent. Every interior cell on a square grid has up to eight neighbours — four cardinal + four diagonal. Corner cells have three; edge cells have five.
This is the single most important fact to internalise. A chain step from cell 7 to cell 8 can go diagonally — which means the gap between two clues can wind through diagonal paths that beginners don't see.
GIVEN NUMBERS ARE ANCHORS — WORK THE GAPS
Every given clue fixes one position on the chain. Treat pairs of consecutive clues as anchors, with a gap of unknown cells between them. If clue A = 10 and the next clue B = 14, then three cells must be placed between them (11, 12, 13).
For each gap, ask: how many cells are reachable from A to B in exactly the right number of diagonal-or-orthogonal steps? If only one spatial route threads between those anchors in the required count, the chain through that gap is forced.
Small gaps (1–2 missing cells between anchors) are almost always forced. Start with those.
LOW-NEIGHBOUR CELLS CONSTRAIN THE CHAIN
Corner cells have only three neighbours; edge cells have five. If a corner cell must be visited (because the chain must pass through every cell), the chain can only enter or leave it via those three neighbours. This severely limits which values can sit in a corner.
Specifically: the values in the three corner neighbours must include both the predecessor (corner value − 1) and the successor (corner value + 1) of whatever number lands in the corner. If no valid pair of predecessors/successors fits in the corner's three neighbours, the corner's value is wrong — backtrack.
Even before placing anything: if you can already see which cells are near a corner, you can sometimes deduce the corner's value range directly from the surrounding clues.
FIND BOTH ENDS OF THE CHAIN FIRST
Cell 1 and cell N² are the chain's termini. Each has only one neighbour on the chain (cell 2 and cell N²−1 respectively). If either terminus is given as a clue, its single chain-neighbour must be in one of the terminus cell's physical neighbours — a strong constraint on a small neighbourhood.
If neither terminus is given, look for cells with very few neighbours (corners, edges) and check whether a terminus placed there would force the first or last few chain values.
THE SOLVING LOOP
- List all gaps between adjacent clue pairs. Sort by gap size — smallest first.
- For each small gap: count the reachable cells between the two anchors (including diagonals). If only one route fits the gap count, place those values.
- After placing, check corners and edge cells touched by the new placements. Use the low-neighbour constraint to eliminate invalid values.
- Recompute all gap sizes with the new information — placements often split a large gap into two smaller, more constrained ones.
- Repeat until the chain is complete.
THE BEGINNER MISTAKE
Forgetting diagonals. Beginners trace paths that look stuck because they're only considering the four cardinal directions. Re-examine any "dead end" by explicitly listing all eight neighbours — one of the diagonal cells usually continues the chain.