In Tetravex, a tile can match one neighbor and still be wrong for its position. Every shared edge must agree, so check the edges around a position together instead of settling for one match.
This guide shows how to narrow down where a tile can go, tell a required border placement from a possibility, and use row and column shifts while tracking the matches they change.
Read the edges, not the whole tile
Each tile has four numbers, one on each edge. A tile's right edge must equal its right-hand neighbor's left edge. Its bottom edge must equal the top edge of the tile below. Edges on the outside of the board have no neighbor and do not need to match anything.
Tiles keep their orientation in Puzzuzu's Tetravex. You cannot turn a top 3 into a left 3 by rotating the tile. If you enjoy placement puzzles that also allow rotation, try Tetra Twirl.
All tiles begin on the board. Drag one onto another to swap their positions, even if they are far apart. A swap is allowed to create mismatches; matching is the victory condition, not a restriction on individual moves. There is no empty cell to maneuver as there is in Classic Slide.
Look for a tile that satisfies two neighbors
Suppose the tile above a position has a bottom edge of 3, and the tile to its left has a right edge of 5. Any tile you put in that position needs 3 on top and 5 on the left. Finding either number somewhere on a tile is not enough.
Scan for the required pair before swapping. If several tiles qualify, compare their remaining edges and the tiles that could go beside them. If none qualifies, at least one of your assumed neighboring placements must change.
This is a small example of constraint propagation. A placement limits the candidates next to it, which can limit the next position in turn. If an earlier placement is wrong, the deductions based on it may be wrong too.
Find edges that must face outward
A top edge can match only a bottom edge on a different tile. If a tile has 4 on top and no other tile has 4 on the bottom, it must go in the top row. The same argument applies to the other three directions.
Two such deductions can identify a corner. A tile that must face outward on both its top and left belongs in the top-left corner. A number that appears only once across the entire set also cannot make a shared edge, so its edge must face outward.
Be careful with the broader advice to “start with the corners.” Corner positions have fewer neighbors, which can actually leave more tiles to choose from. Start with a corner when you have evidence that a particular tile belongs there, rather than because corners are automatically easier to identify.
Count opposite edges separately
Count matching edge values in opposite directions. Four top edges showing 1 and three bottom edges showing 1 imply that at least one of those four top edges must be on the top border. The count alone does not tell you which one.
| Edge count for a value | What you can conclude |
|---|---|
| A top edge has no matching bottom edge on another tile | That tile must go in the top row |
| Four top edges and three bottom edges | At least one of those top edges must face outward |
| Equal top and bottom counts | The counts alone do not identify a border tile |
Make separate tallies for top versus bottom and left versus right. A 1 on a left edge cannot match a 1 on a top edge. Similarly, three occurrences of a number do not imply that the three tiles form a connected group. Some of those edges may face outward, or their orientations may prevent them from meeting.
The coaching overlay uses yellow circles for unequal opposite-edge counts and red circles when no opposite-edge counterpart exists. A yellow circle does not establish that its individual tile belongs on the border. The red glow along a mismatched edge is a different cue. Also, a tile cannot be its own neighbor, so a same-valued opposite edge on that tile is not a usable match for it.
Check both ends of a swap
When you drag a tile into a promising position, the displaced tile moves to the source position. Check both locations afterward. You may improve the area you are studying while breaking a pair elsewhere.
Try building a small group of matching tiles whose placements you can explain. Prefer a tile that satisfies two already-established neighbors over one that gives you a single convenient match. Keep track of which placements are deductions and which are experiments.
If the remaining tiles refuse to fit, return to the earliest uncertain placement bordering that patch. A finished-looking row is not proof that the row is correct. Several arrangements may share those same local matches, and a generated board is not necessarily guaranteed to have a unique solution.
Understand how row and column shifts wrap
The arrow controls beside the board shift a row or column by one cell. A tile that passes the end reappears at the opposite end. Shifting a row right changes the order A B C to C A B.
In that example, the move creates a useful vertical match. It does not solve the row or prove the new placement is final. Before using a shift, predict at least one connection it will make or break.
A row shift leaves the other rows in place, but it changes which tiles sit above and below every tile in the shifted row. It also changes the pair that meets at the wrap point. In A B C becoming C A B, A and B remain neighbors; B and C no longer meet, and C and A become neighbors. Column shifts have the corresponding effect vertically.
The outer controls shift the entire board. They can help reposition an arrangement that is offset, but they still change which edges face outward and which meet across the new internal seam. Always recheck the new neighboring edges. Wrapping is a movement rule; tiles on opposite outer edges are not neighbors for matching purposes.
A useful first solve
Open Random 3×3 and try this sequence of decisions.
- Scan for edges that have no possible opposite-edge partner. Use those to establish any forced border positions.
- Find a position beside two placements you have reason to trust. Search for a tile matching both required edges.
- Before swapping it in, inspect what will happen at the source position too.
- If several candidates work, try one and remember the choice. Backtrack when it leaves a neighboring position with no candidate.
- Use a row or column shift when you can explain the resulting connections, then inspect the changed seams.
Puzzuzu generates random tile sets from a matching arrangement, so they have at least one solution. That does not make every locally matching patch extendable into a complete solution. Keep testing the surrounding edges as the patch grows.
Additional resources
- The GNOME Tetravex instructions explain the standard edge-matching game. Its separate tile pool differs from Puzzuzu's board of swappable tiles.
- UC Berkeley's introduction to constraint satisfaction explains variables, candidate values, and constraints. Board positions and candidate tiles are a concrete example.
- UC Berkeley's guide to solving constraint problems develops backtracking and choosing the most constrained variable next.
- The Puzzuzu glossary explains backtracking, heuristics, and the distinction between finding a solution and finding an optimal one.
Start in the Easy Random collection. Aim to explain why a tile belongs before you place it. Once you can track those reasons across a small board, try a larger one in the Hard Random collection.