STEP 1 — LIST ALL GIVEN CLUES AND SORT THEM
Before placing a single number, write down every given clue in ascending order. The path visits every cell exactly once, so the sequence must be consecutive from 1 to the total cell count. Each pair of adjacent clues defines a gap: the clue values tell you how many missing numbers sit between them.
STEP 2 — FIND GAP-1 SEGMENTS (ADJACENT CLUES)
A gap of 1 means two consecutive clues must occupy neighbouring cells. Check whether the two clue cells are already adjacent — if so, that segment is trivially closed. If they are not adjacent, the path between them is forced through any shared neighbours. Mark those cells immediately.
Gap-0 is impossible: two clues with the same value mean the puzzle has no solution (check your read). Gap-1 between non-adjacent cells with no common neighbour is also impossible — useful for ruling out placement errors.
STEP 3 — EXPLOIT LOW-NEIGHBOUR EDGE CELLS
Interior hexes have six neighbours; edge hexes have four or fewer; corner hexes have two or three. Any clue on a corner cell has a very small route set — trace those first. If a clue's position limits the next or previous step to a single available hex, that step is forced.
A hex with only one unvisited neighbour that the path must pass through is a dead-end forcing: the path must enter and exit through that bottleneck.
STEP 4 — TRACE SHARED NEIGHBOURHOODS BETWEEN CLUES
Pick any two clues that are 2 or 3 apart in value. List the neighbours of each. If the path between them must pass through cells that are common neighbours of both clues, those intermediate cells are forced regardless of which route you take. Place them.
This is especially powerful when one clue has few free neighbours: the overlap between a constrained clue and its nearest partner is almost always a forced segment.
STEP 5 — USE CONNECTIVITY AS A FILTER
The path visits every cell exactly once and must remain connected. If a tentative route would cut off a cluster of unvisited cells from the rest of the path, that route is illegal. Use this to eliminate candidate placements even before you can positively force a cell.
After placing a segment, quickly scan for isolated pockets — any group of unvisited cells with fewer entry points than needed to route through them.
SOLVING ORDER
- List clues, compute all gaps.
- Place gap-1 forced segments.
- Trace corner and edge clues (fewest neighbours).
- Apply shared neighbourhood forcing for gaps ≤3.
- Use connectivity to eliminate bad candidates.
- Repeat until solved.
Most beginner puzzles solve in two or three passes through steps 2–4 without ever needing a guess.
BEGINNER TRAP — COUNTING GAPS FROM THE WRONG END
If clue A = 5 and clue B = 9, the gap is 3 (cells 6, 7, 8 sit between them), not 4. Count the cells between the clues, not the difference between the clue values, and not including the clue cells themselves. Miscounting by 1 here misplaces an entire segment.