Tents: pairing trees and tents
Each tent belongs to one tree. When a tree has only one place for its tent, that tent is taken, and the trees around it have to look elsewhere.
How it works
The rules pair trees and tents one to one. Every tree has its own tent beside it, and no tent is shared. Solvers call this pairing.
Pairing turns counting into certainty. If a tree has only one open square beside it, its tent goes there, and that tent now belongs to it. Any other tree touching the same tent can’t use it, so that tree’s tent must be one of its other neighbors.
It also makes grass. A square whose trees all have their tents already can’t hold a tent, because the tent would have no tree of its own.
Grass from pairing
On the board below, row 6, column 4 sits beside one tree, at row 6, column 5. That tree already has its tent at row 6, column 6.
A tent at row 6, column 4 would need a tree of its own, and none is left. So the square is grass.
Why it holds
Suppose a second tree used the taken tent. Then that tent would belong to two trees, and some other tree would be left without one, since there are exactly as many tents as trees. That breaks a rule, so it can’t happen.
Worth memorizing
A tree with one open neighbor claims it.
Pitch the tent and pair them.
A paired tent is off limits to other trees.
Their tents are among their other neighbors.
A square whose trees are all paired is grass.
Practice
0 of 3 rightWhich square holds the tent for the ringed tree at row 2, column 5?
Which open square is grass because the only tree beside it already has its tent?
A tent touches two trees. How many of them can it belong to?