Tents and Trees strategy: ten techniques, with worked boards

Technique 1 · basic

No tree, no tent

Every tent belongs to a tree directly above, below, left or right of it. So a tile with no tree on any of its four sides can never hold a tent, whatever the numbers say. Diagonal trees don't help: a tree touching a tile only at a corner is not its neighbor. On a fresh board this is always the first sweep, and it usually clears a third of the open tiles before you have read a single number. Work it as a scan, tree by tree, rather than tile by tile: the tiles that survive are exactly the up to four sides of each tree.

The open tiles that remain are your candidates. Every later technique works only on them, so a clean first sweep makes the counting easier. Look closely at board corners and long empty stretches between trees, where whole runs of tiles drop out at once.

Technique 2 · basic

Zero rows and columns

A 0 beside a row or above a column means that line holds no tents at all. Every open tile in it is grass, including tiles right next to a tree. This is the cheapest deduction on the board, and it is easy to skip because the 0 sits outside the grid. Do it straight after the first sweep. A 0 line often takes away one or two sides of the trees inside it or beside it, and that is what sets up the later moves: a tree that loses sides to a 0 is on its way to having only one free side left.

A 0 also decides things next door. A tree inside a 0 row has to take its tent from the row above or below, so that tent pushes on the count of a neighboring row before you have placed anything.

Technique 3 · basic

Grass around every tent

Tents never touch, not side by side and not at a corner. The moment you pitch a tent, all eight tiles around it are grass. Mark them at once, every time, even when it feels obvious: those grass marks are what take sides away from the neighboring trees and make the next tent appear. A tent beside a board edge clears five tiles, a tent in a corner three, a tent in the middle up to eight. Solvers who skip this step end up with a board full of tents and no idea where the next one goes.

The no-touch rule also cuts across rows. A tent in one row blocks three tiles in the row above and three in the row below, which is why one tent can finish a neighboring row's count without touching it.

Technique 4 · basic

A tree with one free side

Each tree needs its own tent on one of its four sides. Board edges, other trees and grass take sides away. When a tree that still has no tent is down to exactly one open side, its tent goes there. This is the move that places most tents on easy and medium boards. Check it every time grass appears next to a tree, because a single new grass mark can be the one that leaves a tree with one option. Trees in corners start with only two sides and trees on an edge with three, so look at them first.

A tree that stands next to another tree has lost that side too. Pairs and clumps of trees are where single free sides appear early, often right after the first sweep and the zero lines.

Where to look: trees in a corner or on an edge, trees beside other trees, and trees next to a line with a 0.

Technique 5 · basic

A full row means the rest is grass

Count the tents already standing in a row or column and compare them with its number. When they match, the line is done, and every open tile left in it is grass. This is the zero rule again, for lines that reached their number instead of starting at it. It fires all the time in the middle of a solve, usually right after a tent is placed by another technique. Make it a habit: each time you pitch a tent, glance at the number for its row and its column before you do anything else.

Technique 6 · basic

Open tiles that match the count

This is the mirror image of the full row. Take a row or column, subtract the tents it already has from its number, and count its open tiles. When the open tiles equal the tents still needed, every one of them is a tent. It shows up most in lines with a large number, like a 3 on a 6 by 6 board, once the first sweep and the zero lines have cleared the rest. It is the simplest case of the gap count in technique 8: every open tile is a run of its own.

Once the tents are in, go straight back to technique 3. Three new tents in one row put grass on most of the row below, and that usually hands you the next tree with one free side.

Technique 7 · intermediate

Pairing trees and tents

Each tree gets exactly one tent, and each tent belongs to exactly one tree. Keep track of the pairs. A tent that touches only one tree belongs to that tree, and that tree is now done. Any open tile whose only neighboring trees are already done can't hold a tent, because that tent would have no tree left to belong to. This is the technique beginners miss most, because the grid has no mark for pairs: you have to see them. A tile that touches two trees stays open until both of them are paired.

Pairs also tell you which trees are still waiting. A tent beside two trees settles only one of them. Until a second tent appears next to the other tree, keep that tree's open sides in play and don't mark them as grass yet.

Technique 8 · intermediate

Count the gaps in a row

Tents in the same row can't sit side by side, so a run of open tiles holds fewer tents than its length. A run of 1 or 2 tiles holds at most one tent, a run of 3 or 4 at most two, a run of 5 at most three. Split a row's open tiles into runs, add up the most each run can hold, and compare with the tents the row still needs. When the total equals the need, every run is full: a run of 1 gets its tent, a run of 3 gets tents on both ends.

Runs also reach into the next row. When a run must hold a tent but you don't know where, any tile in the row above or below that every possible spot would touch is grass. A run of 2 that needs one tent makes the two tiles directly above it and the two below it grass.

Where to look: rows and columns with a number of 2 or more, and open tiles split into a few short runs.

Technique 9 · intermediate

The shared corner

Look at a tree with exactly two open sides that meet at a corner, for example the left and the bottom. Its tent goes on one of them, you don't know which yet. But the tile diagonally between them, below left of the tree, touches both. Whichever side gets the tent, that tent will touch the corner tile, so the corner tile is grass. You place nothing, yet you gain a grass mark, and that mark can leave another tree with one free side or finish a row count.

It doesn't work for a tree whose two open sides are opposite each other, above and below, because no single tile touches both. The trick needs two sides at a right angle.

Technique 10 · advanced

Two rows counted together

When every single row and column is stuck, read two neighboring rows as one band and add their numbers. Then ask which layouts of that many tents fit into the band with no two touching, including diagonally across the two rows. Tents in one row block three tiles in the other, so there are often only a handful of ways. A tile every layout uses is a tent, a tile no layout uses is grass. On hard boards it is the cleanest way forward once single lines run dry.

Start from the row with the larger number, since it has fewer ways to fit. Try each way briefly and check whether the other row still has room for its tents. Columns work the same way: pair two neighboring columns.

Where to look: two neighboring rows whose numbers add up to 3 or more, where the busier row has few open tiles.

Common mistakes

• Forgetting the diagonal. Tents can't touch at a corner either. Grass the four diagonal tiles around a new tent along with the four sides.
• Treating a diagonal tree as a neighbor. A tent must be above, below, left or right of its tree. A tree at the corner of a tile doesn't count.
• Giving one tent to two trees. A tent next to two trees still belongs to only one of them. The other tree needs a tent of its own.
• Guessing when stuck. Every Campfire puzzle has one answer that logic reaches. Recount the full rows and look for a shared corner or two rows to count together before you try anything else.