Tents: testing a square
When counting stalls, suppose a tent on one square and put grass around it. If a row, column or tree runs out of room, the square is grass.
How it works
Tents can’t touch, so a line can’t hold tents side by side. A run of open squares holds at most half its length, rounded up. Three open squares in a row can take two tents, on the ends, and two open squares can take only one. Solvers call this the line’s room.
A tent takes room from its neighbors. Its grass covers up to three squares in each neighboring row and column. So suppose a tent on a square, put grass around it, and count again. If some row or column now has less room than the tents it still needs, the tent can’t go there. The square is grass. That is proof by contradiction.
Sometimes nothing breaks right away. Then follow it through: make every move the supposed tent forces, using the counts and the pairs, until something breaks or the moves run out.
Which squares to test
Test squares next to a line that is short of room. A tent in the row above or below covers up to three of its squares.
Also test squares beside a tree with two open sides. A tent on one side takes the other side’s room from the lines around it.
Test tents, not grass, first. A tent changes nine squares at once, so it breaks things faster.
Why it holds
The puzzle has one solution. If a tent on a square forces a broken count, that tent is not part of the solution, so the square is grass. The chain of forced moves is just more of the same rules, applied in order.
Worth memorizing
A run of open squares holds at most half its length, rounded up.
Tents in a line can’t sit side by side.
Suppose a tent, add its grass, recount.
A line short of room means the square is grass.
If nothing breaks at once, follow the forced moves.
Stop when something breaks or the moves run out.
Practice
0 of 3 rightSuppose a tent at row 2, column 5. How many open squares would row 1 have left?
Row 3 has open squares at columns 4 and 7, with grass between them. How many tents could those open squares hold at most?
You suppose a tent on a square and follow the forced moves, and nothing breaks. What do you know?