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Today's medium 10×10 Slitherlink puzzle has 1 zero-cell, 7 three-clue cells, and a closed loop of 108 edges. Below is a complete walkthrough — every edge deduced in order, with the reasoning shown step by step. Work through it once and you'll have the full toolkit for puzzles like this one.
Study the clue numbers before making any marks.
Scan the grid before drawing anything. This 10×10 puzzle has 1 zero-clue cell at (row 9, col 3). A "0" means the loop cannot cross any of its four sides — mark every adjacent edge ✗ immediately. No reasoning required: that's 4 free eliminations from a single pass.
Now look at what changed for the neighbors. Cells at (row 9, col 2), (row 9, col 4) each lost one or more unknown edges. The moment a cell's remaining unknowns match its clue number, every one of those unknowns must be a line. When its confirmed lines already equal its clue and unknowns remain, those unknowns are all ✗. That's the cascade — the zeros did the work.
★ Take this with you: always mark zero-adjacent edges ✗ before touching anything else. The downstream cascade — neighbors losing unknowns until they lock — typically resolves 30–50% of the puzzle before you apply a single other rule.
After zeroes, check the four grid corners. A corner cell only touches 4 edges — and 2 are along the boundary, already constrained by the grid edge. That reduced freedom makes corner clues resolve faster than any interior cell.
bottom-right corner (row 10, col 10) has clue 3: it needs 3 lines from 4 edges, but 2 of those edges are along the grid boundary. That forces BOTH boundary edges to be lines right now — 2 confirmed in one step, before touching any neighbor.
★ Take this with you: corner cells are your second stop after zeroes. A clue-3 corner hands you 2 confirmed lines for free. Even a clue-1 corner is a hair-trigger — set it up now, and it fires the moment any one neighbor is resolved.
This puzzle has 7 three-clue cells — 6 interior: (row 1, col 8), (row 4, col 2), (row 5, col 1), (row 8, col 8), and 2 more. A "3" means only one of the cell's four edges is excluded from the loop. The moment any one of its edges is marked ✗ — by a zero-cell cascade, a border constraint, or a corner deduction — the other three are immediately forced to be lines. That chain fires fast once the earlier steps have done their work.
The vertical 3-3 pair at (row 9, col 6) and (row 10, col 6) gives us an even sharper shortcut. These two cells share one boundary edge — but notice: whether that shared edge is a line or a ✗, both cells still need the 3 outer edges to be lines. So mark all the outer (non-shared) edges as lines immediately, without even deciding the shared one. That's 6 confirmed edges from one observation.
★ Take this with you: scan for 3-cells immediately after corners. And when two 3-cells are adjacent, use the pair rule — you don't need to know the shared edge to lock the outer ones.
The puzzle has 16 one-clue cells at (row 1, col 7), (row 3, col 1), (row 3, col 4), (row 3, col 8), and 12 more. A "1" does nothing on its own — but after the earlier steps eliminated edges from neighbors, each of these cells now has fewer unknowns. When a 1-cell reaches exactly 1 unknown edge remaining, that edge is forced to be a line. When it reaches exactly 3 crossed edges, the last unknown is forced to be a line too.
The 23 two-clue cells — including (row 1, col 2), (row 1, col 5), (row 1, col 9), and 20 more — are the mid-game engine. Each needs exactly 2 edges as lines. By themselves they're ambiguous: the two lines could be opposite edges (straight pass) or adjacent edges (corner turn). But once a zero-cascade or 3-cell deduction marks one of a 2-cell's edges ✗, the remaining edges narrow fast. When 2 edges are ✗ and the clue is 2, both remaining unknowns snap to lines immediately.
★ Take this with you: after the opening wave (zeroes + threes), pause and scan every 1-cell and 2-cell. Check how many unknowns each has left. Any cell where unknowns equal its clue — or where crosses equal 4 minus its clue — is fully determined right now. This 30-second scan often unlocks 5–10 edges in one sweep.
The 4 edges resolved above cover the mechanically derivable deductions. At some point in this 10×10 medium puzzle, the direct rules stop firing — every remaining unknown edge has two or more possibilities when looked at in isolation. This is not a signal to guess. It's a signal to zoom out.
Here's the move: trace every confirmed line segment and find its open endpoints (dots with exactly 1 known line). These are the places the loop must continue from. Now ask: if I were to connect two nearby open endpoints, would that form a closed ring while any clue cells outside the ring are still unsatisfied? If yes, that connection is ✗ — premature closure is illegal. Mark it, and watch a new wave of propagation begin.
If that doesn't fire, do one more pass: find any cell where remaining unknowns = clue value. Those unknowns are all lines. Find any cell where confirmed lines = clue value and unknowns remain — those unknowns are all ✗. In this puzzle, this pass breaks the deadlock completely.
★ Take this with you: when direct rules stall, don't guess — trace open chain ends. The loop's global single-path constraint forbids premature closure, and that constraint alone often forces the next 5–10 edges.
The loop for this puzzle runs 108 edges — a single unbroken path that closes on itself and satisfies every numbered cell exactly. Here's how the endgame resolves.
As the final unknowns narrow down, two open chain ends approach each other. Before connecting them, check: are all clue cells already at their required line count? Any cell still short would be left outside the ring — so that closing edge is ✗, not a line. Mark it, watch the last edges snap into place through the vertex rule, and then the correct closing edge becomes the only option.
Every deduction above — zero cascades, corner locks, 3-cell fires, vertex chains, premature-closure blocks — led to this single verified solution without a single guess.
★ Take this with you: in the endgame, never close a loop without checking that ALL clue cells are satisfied inside it. One unsatisfied cell outside = that closing edge is ✗. This single check resolves the final ambiguity in almost every medium and hard Slitherlink puzzle.
About this analysis
Every step above is derived from solving this specific puzzle using a constraint-propagation engine that applies the same techniques competitive Slitherlink solvers use: zero-cell elimination, three-cell forced edges, corner locks, vertex connectivity, and loop-closure detection. No generic templates — the deduction chains, cell coordinates, and clue counts you see here reflect the actual logic path through this puzzle.
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