How to solve Tents: a tent for every tree

The rules

• Every tree has exactly one tent directly above, below, left or right of it, and every tent belongs to one tree.
• Tents never touch, not even diagonally.
• The numbers outside the grid give the number of tents in each row and column.

Find the grass first

• Rows and columns with a 0 get no tents: mark them all as grass.
• Cells not next to any tree (above, below, left or right) can never hold a tent: mark them as grass.
• A tree's diagonal cells don't help it: a tent must share a side with its tree, so only its four side cells are candidates.

Trees with only one spot

Once the grass is marked, look at each tree's four side cells. If only one is still free, the tree's tent goes there. Place it, then mark the eight cells around the tent as grass, because no other tent may touch it.

Be careful with trees that share free cells: two trees side by side with one free cell between them can't both use it. Each tent belongs to exactly one tree.

Use the row and column numbers

• When a row already has as many tents as its number, the rest of the row is grass.
• When a row's free cells exactly match its number, every free cell is a tent.
• A row that needs two tents in a stretch of three free cells must use the two ends, because the middle would touch both.

A solving routine

1. Mark every 0 row and column, and every cell that touches no tree, as grass.
2. Place tents for trees with only one free side cell, and grass around each tent.
3. Finish rows and columns whose counts are complete or exactly matched.
4. Pair trees and tents so no tent is shared, and repeat.

Practise

On Puzzimo, tap a cell to mark it as grass ▪ (tap again to clear), double-tap to pitch a tent ⛺, and drag to mark many cells at once. A tent where the solution has none counts as a mistake: it's shown and turned into grass, and the third ends the round. Boards come in 8×8, 10×10 and 12×12, with an 8×8 daily challenge.

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