A tree cannot pair with a diagonal tent in Tents Puzzle. Pairing is strictly orthogonal, which means the tent must share a top, bottom, left, or right edge with its tree, and a diagonal corner touch never counts as a valid match. The five-by-five board in Tents Puzzle holds four fixed trees and asks you to add four tents, and the browser checks every placement against that exact rule using a bipartite matching test before it accepts the board. If a tent touches a tree only at a corner, the puzzle treats it as an unpaired orphan and flags a contradiction until you move it to a side-sharing cell. This single rule is the most common point of confusion for new players, and it is also the rule that makes the rest of the logic work, because once every tree claims exactly one orthogonal neighbor as its tent, the no-touch constraint can propagate cleanly across the grid. The same restriction applies in reverse: a tent must not touch another tent in any of the eight surrounding cells, including diagonals, so two diagonally adjacent tents are also illegal even when no tree is involved.
What "Orthogonal Pairing" Actually Means
In everyday language, two squares are adjacent when they touch, and most people instinctively count diagonal corners as touching too. Tents Puzzle uses a stricter definition borrowed from graph theory: orthogonal adjacency means sharing a full edge, not a single corner. For any tree on the board, there are exactly four orthogonal neighbors, one in each cardinal direction, and any one of those four can host that tree's tent. The remaining four diagonal corners of the same tree are off-limits for pairing even though they sit right next to the tree visually. The distinction matters because the puzzle validates placements by running a bipartite matching pass that only allows tents to claim an adjacent tree when an edge in the cardinal direction connects them. Visually this is easy to miss when two cells look like they are touching, but the rule treats edge-sharing and corner-sharing as completely different relationships. The five-by-five grid in Tents Puzzle labels each cell with its row and column and announces its current state, so you can confirm at any moment whether a placement is being recognized as a pair or rejected as an orphan placement.
All Eight Neighbors at a Glance
The table below shows every cell that touches a single example tree and whether the puzzle will accept a tent there as that tree's pair. Edge-sharing cells pair; corner-sharing cells do not. The same eight-cell pattern surrounds every tent and is used to enforce the separation rule.
| Relative Position | Touches the Tree at | Counts as a Pair |
|---|---|---|
| Top neighbor | Shared bottom edge | Yes |
| Bottom neighbor | Shared top edge | Yes |
| Left neighbor | Shared right edge | Yes |
| Right neighbor | Shared left edge | Yes |
| Top-left corner | One corner point | No |
| Top-right corner | One corner point | No |
| Bottom-left corner | One corner point | No |
| Bottom-right corner | One corner point | No |
Why the Validator Rejects Diagonal Tents
The validator runs after every tent action and checks four conditions in sequence. First, every tent must be on a non-tree cell and not in a position that would push its row or column past the edge clue. Second, no tent may share an edge or a corner with another tent. Third, each row and column must end with the exact count shown on its edge. Fourth, a bipartite matching check has to confirm that each tent can be assigned to a distinct tree through one of the four cardinal edges. The diagonal rule falls out of that fourth check: a tent that touches only the corners of nearby trees cannot be wired to any of them, so it counts as an orphan and the validator marks a contradiction. Removing the offending tent clears the flag and lets you try a different cell. This is the same logic published for the canonical Tents rules in Simon Tatham's Portable Puzzle Collection documentation, where the only allowed tree-tent contact is up, down, left, or right. The browser version uses the same definition, which keeps the puzzle consistent with every other standard Tents implementation you may have played.
How to Pair Every Tree With One Orthogonal Tent
Open Tents Puzzle and the cursor sits on the first cell. The fixed five-by-five grid shows four tree characters in their permanent positions, and the remaining cells are empty. Follow these steps to pair every tree with one orthogonal tent and complete the board.
- Use the arrow keys to move the cursor to a non-tree cell that sits directly above, below, left, or right of one of the four trees.
- Press Space to drop a tent on that cell. If you change your mind, press Space again on the same cell to remove it.
- Watch the live counts above the board update. The current tent total and the matchable tent total should rise together when you place a tent next to a tree.
- Keep every new tent separated from existing tents in all eight surrounding cells. The validator flags a contradiction when a placement would create a diagonal corner touch or an edge touch between two tents, but the placement stays editable and you can remove the tent to clear the warning.
- Stay inside each row and column clue. If a row is marked with a 1 and a second tent appears in that row, the validator flags a contradiction that you can correct by removing the second tent.
- Press Enter on an empty non-tree cell to add or remove a grass note for cells you believe cannot hold a tent. Grass is optional reasoning and does not affect validation.
- Continue placing tents until all four trees have one orthogonal match, every row and column matches its edge clue, and no two tents touch. The fixed solution places tents at cells 1, 8, 15, and 22 in zero-based order for a 960-point score.
Every action above is reversible, and a contradiction never ends the board. Remove the tent that triggered the warning and try the next cell. The browser recalculates the whole rule set after every change, so the live counts above the board are always the authoritative source of truth for the current state.
Edge Clues and the Separation Rule Working Together
Each row and column carries a small number on the outer edge that tells you exactly how many tents that line needs. A 1 means a single tent, a 0 means the line stays empty, and any number up to the line length gives you a hard target. The board shows two numbers per line: the edge clue and your current count. When the two match, the line is satisfied. When your count is higher than the clue, the validator raises a contradiction and you must remove the tent that pushed it past the limit. When your count is lower, the line is still open and you keep looking for valid placements. The edge clues and the orthogonal pairing rule work together. A row might allow only one tent, but that tent still has to claim an orthogonal tree. If every adjacent tree in that row is already matched, the row simply must stay empty. The constraint cascades across the grid: as you satisfy one row, you may close off entire columns, and the puzzle resolves quickly when you trust both the clue numbers and the adjacency rule at the same time.
Common Mistakes Around the Diagonal Rule
Three diagonal mistakes trip up new players. The first is treating a tent that touches a tree at one corner as a valid pair; the validator flags it as an unpaired tent because the tent cannot be matched through a corner, and you remove the tent to clear the contradiction. The second is allowing two tents to touch diagonally; the rule that separates tents applies in all eight surrounding directions, not just the four orthogonal ones, so corner contact between two tents is the same kind of violation as edge contact. The third is using the no-touch rule for tents while forgetting the orthogonal rule for tree-tent pairs; the two have to be applied independently, and a placement that satisfies one can still violate the other. Other mistakes include placing a tent on a tree cell (which does nothing), marking grass on a tree cell (which also does nothing), or exceeding the row or column count while chasing a matching tent. Each of these mistakes is reversible: the board stays editable through any contradiction, and removing the offending tent clears the warning so you can keep working the puzzle.
Related Fixed Logic Puzzles
Tents Puzzle uses a tight set of rules that reward careful placement and pattern reading. If you enjoy the orthogonal pairing logic, Numberlink Puzzle extends a similar adjacency idea to continuous orthogonal paths between number pairs. If the separation rule appeals to you, the Battleships Puzzle Tips and Tricks guide covers the same diagonal prohibition for ship pieces and explains how to read edge clues efficiently across rows and columns. None of these share the exact orthogonal pairing rule, but each one trains the same discipline of reading small constraints carefully and refusing to accept corner contact as a real connection.