How to solve Tents
Every tree gets one tent beside it, tents never touch, and the numbers count tents per line. Grass the squares no tent can use, then let the counts do the work.
How it works
Each tree needs one tent on a square beside it: above, below, left or right. Each tent belongs to exactly one tree, so there are as many tents as trees. Tents can’t touch each other, not even at a corner. The numbers outside the grid count the tents in each row and column.
Start by marking grass on every square that has no tree beside it. Then use the counts. A row that has all its tents gets grass in the rest. A row with exactly as many open squares as tents it still needs gets tents in all of them. Every tent you pitch puts grass on its eight neighbors.
When counting stalls, test a square. Suppose a tent there, add its grass, and see if some row or column runs out of room. If one does, the square is grass. That is proof by contradiction, not a guess.
Where to look first
Rows and columns marked 0 are all grass. So is every square that doesn’t touch a tree along a side.
Then look for lines where the open squares barely fit the count. In a line that needs two tents, three open squares in a row can only take tents on the two ends.
Trees in a corner, or hemmed in by grass, often have only one open neighbor. That neighbor is their tent.
Worth memorizing
One tent per tree, beside it.
Above, below, left or right, never diagonal.
Tents never touch.
Put grass on all eight neighbors of every tent.
A line with all its tents is grass everywhere else.
A line with just enough room is tents everywhere open.
Practice
0 of 3 rightBefore you place anything, which of these squares must be grass?
Column 5 needs two tents and has one. Where does the second go?
Row 4 has its one tent. What goes in its other open squares?