Choose your next step in a 3 by 3 pipes puzzle by rotating the corner and edge tile with the fewest still-valid orientations, then read the live loose-end count after every press of Space or Enter to confirm each move decreases mismatches without forming a cycle. In the Lizely Pipes Puzzle, every tile stays in its cell and only its orientation changes, so the decision at any moment is not where to put a pipe but which of the remaining rotations for the currently selected tile is still legal under the four published rules. Those rules are checked automatically after every rotation: no opening may point outside the grid, every opening must meet a reciprocal opening on the neighboring tile, all nine tiles must belong to one connected component, and that component must be acyclic. The disclosed target on this 3 by 3 board is a snake with nine vertices and exactly eight reciprocal edges, so any move that would create a ninth edge or split the network should be skipped even if it satisfies the boundary tests.
The Lizely board uses a fixed scramble, a fixed score formula, and a fixed target network, which is why a repeatable sequence of 18 clockwise rotations solves it from the published starting orientations. The work below explains each rule in enough detail to choose your next rotation confidently, the order in which to read the tiles, and how to read the feedback the board shows after every press.
What "Choosing Your Next Step" Means in a 3 by 3 Pipes Puzzle
Pipes Puzzle belongs to the family of connection games also called Net, FreeNet, or NetWalk, and the published 3 by 3 board follows the maintained rules from Simon Tatham's Portable Puzzle Collection and the independent Puzzolve guide. The single decision a player faces at any moment is which of the up to four orientations for the currently selected tile is still legal. There is no swapping, no sliding, and no movement between cells. Every tile stays exactly where it sits; only the rotation changes.
That changes the shape of the decision. You are not placing a piece on an empty square; you are narrowing an orientation until one of four conditions goes false. The board runs the validation after every rotation, so the right way to choose the next step is to watch the feedback it gives you rather than to plan several moves ahead. Each rotation either tightens the loose-end count, keeps it flat, or pushes it back up. The looser the board becomes after a move, the more likely you have chosen the wrong orientation.
The Lizely implementation pins this further. There is no random generator, so the opening scramble is the same on every load. There is also a fixed score formula and a fixed target network — the snake described in the product contract — which means the sequence of correct rotations is reproducible for anyone who wants to verify a route.
The Four Checks the Browser Runs After Every Rotation
Every press of Space or Enter triggers four automatic checks, and understanding each one is the only way to predict which of your next steps will be accepted. The board stores each pipe as a four-bit mask with 1 for up, 2 for right, 4 for down, and 8 for left, and a rotation shifts that mask clockwise while leaving the cell and the number of openings unchanged.
The first check is for outward openings. If any bit points at a row or column that falls outside the 3 by 3 grid, the status line counts that opening as a loose end. The second check confirms reciprocity: every opening must face a neighbor whose opposite side carries the matching bit. An opening facing a wall that does not open back is recorded as a mismatch.
The third check counts connectivity. Reciprocal openings are added to an undirected adjacency graph, and a breadth-first traversal from the first tile reports how many of the nine cells are reachable. The fourth check rejects cycles. With nine tiles, a single connected network must contain exactly eight reciprocal edges to be acyclic; a disjoint-set check identifies any link that would join two vertices already in the same component as a cycle, which would push the edge count to nine and fail the acyclic requirement. Completion therefore requires zero mismatches, all nine tiles reachable, exactly eight edges, and no cycle.
Corner-First, Edge-Second, Center-Last: A Reading Order That Works
A practical move order starts where the board has the least freedom. The four corners of the 3 by 3 grid each sit against two outer walls, so any pipe opening on a corner that points up, down, left, or right toward a boundary must be rotated inward. On most pipe shapes that leaves only one or two orientations out of four still viable, which is why corner loose ends are the fastest way to lower the status count.
The edge tiles — the four cells that touch one outer wall each — get visited next. They have three viable rotations instead of one or two because only one of their four sides faces the boundary. By the time both the corner and its adjacent edge are oriented, the center of the board has often reduced to a single candidate orientation, because the openings forced inward from the corners and edges leave one matching rotation open.
The center tile is the last to move, and it is also the one most often rotated twice. Because it has no outer walls to satisfy, its first move is sometimes chosen for cycle prevention rather than for matching, and a cycle correction shows up as a small rise in the loose-end count that the next rotation undoes. Reading the tile in this order — corners, edges, center — is one reading order that works on the Lizely 3 by 3 snake fixture.
How to Pick, Rotate, and Restart in Pipes Puzzle
- Press an arrow key to move the highlighted cursor to the tile you want to read. The cursor stops at every board edge and never wraps, so pressing Right on the rightmost column is ignored.
- Read the tile's current pipe shape from the line glyphs and note which of its four sides carry an opening.
- Press Space or Enter to rotate the selected tile clockwise by 90 degrees. The cursor stays on the same cell, and the rotation is the only change.
- Mouse and touch users can click or tap any tile directly to rotate that tile without moving the cursor first.
- Watch the status line below the board for two figures: the loose-end count and the number of cells reachable from the first tile. A move that drops the loose-end count without dropping the reachable count is a good next step.
- If the loose-end count rises, press Space again to rotate the same tile back, or move the cursor to a neighbor and try a different orientation. The board remains editable even when an orientation is unsolvable from the current state.
- When the board reports zero loose ends, nine reachable cells, and exactly eight edges, rotations freeze automatically to keep the solved network stable. Press the Restart control to restore the original scramble, the cursor position, the starting score of 1,000, and the live counters.
Reading the Live Status Line Before You Commit
The status line is the only feedback the board offers during play, so each of its two numbers deserves attention. The loose-end count is the number of openings that either point outside the grid or face a neighbor without a reciprocal opening. Reaching zero means every pipe meets a matching opening on its neighbor, or has no openings facing that side at all.
The connected-cell count starts at the first tile and grows as reciprocal edges join more tiles into the same component. Once the count reaches nine, the network spans every cell on the board. If it stalls below nine after several rotations, two or more groups are still isolated, and the next move should join them through a tile that touches both.
| Status reading | What it means | Next move |
|---|---|---|
| Loose ends increasing | The last rotation opened a new outward side or broke a reciprocal edge | Press Space again on the same tile, or move to a neighbor |
| Loose ends unchanged | The rotation was valid but made no progress | Pick a different tile, especially a corner that still faces outward |
| Loose ends decreasing | The last rotation closed a mismatch | Continue toward the smallest loose-end count |
| Connected cells = 9, loose ends = 0 | The network spans every cell with no mismatches | Check the edge count before declaring the board solved |
A useful local rule is that a move which drops the loose-end count by exactly two and raises the connected-cell count by one is almost always a correct next step, because it removed one outward opening and one mismatch while linking a new tile to the main group. A move that drops the connected-cell count is a cycle correction in disguise — the previous move had already joined everything, and the current move is breaking a reciprocal edge. Undo it by rotating the same tile again.
Why Exactly Eight Edges and One Loop-Free Network
The constraint that the network stay loop-free is not arbitrary. With nine tiles in a connected acyclic graph, the edge count is forced by the formula for trees: edges = vertices − 1. Nine tiles minus one is eight reciprocal edges, which is the same eight edges the disclosed target network contains on its way through every row of the board.
This is why the cycle check matters even when the loose-end count reads zero. A configuration with zero mismatches, nine connected tiles, and nine edges would still be invalid because the ninth edge closes a loop. The disjoint-set check the browser runs is the structural form of the same rule: a link that joins two tiles already in the same component is rejected. Reading the board as a tree rather than as a grid makes the next step obvious — every new link should grow the tree, never close it.
Scoring, the 18-Turn Route, and When to Restart
The Lizely board scores each rotation against the fixed target network. The starting value is 1,000 and each clockwise rotation subtracts 10 points, so the formula is max(0, 1000 − 10 × rotations). The disclosed scramble on the 3 by 3 snake fixture takes exactly 18 clockwise rotations to undo from the published starting orientations, which gives the player a final score of 820 points — 1,000 − 10 × 18 = 820 — when every move is on the optimal route.
If at any point your moves drift past the optimal route, the score reflects it: one extra rotation costs ten points, and four extra rotations cost forty. Pressing Restart restores the original scramble, the cursor position, the starting score, and the live analysis counters, so an unsuccessful attempt is recoverable rather than permanent. A best score is the only value the board writes to localStorage, and only when the network reaches the solved state.
For a short spatial-network break, count your loose ends, pick the corner with the most outward openings first, and let the status line confirm each move before you commit the next rotation on the Lizely Pipes Puzzle.
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