How to solve Tents and Trees
This puzzle is a square grid with a tree standing in some of the cells and a number beside every row and every column saying how many tents that line holds. You pitch the tents so that every line holds exactly its number, so that no two tents touch — corners included — and so that the tents and the trees pair off one to one, each tent directly beside its own tree.
Nothing here is a hint: the board never checks you against the answer, and none of the moves below needs it to. These three techniques are the whole ladder the boards are graded on, simplest first, and each is drawn on a 6 × 6 — smaller than any board the game deals, because a picture that fits in one look teaches better than a true-to-size one and nothing in these moves depends on the size.
How to play
The number beside a row or column says how many tents it holds.
Every tree has a tent of its own directly beside it — above, below, left or right, never across a corner — and every tent belongs to one tree.
No two tents may touch, not even at a corner.
Crosses are your own notes of where a tent cannot go; only the tents are the answer.
Tap a cell to cross it out, tap again to pitch a tent, once more to clear it. Drag across cells to cross out several at once.
A tent turns red when it touches another, when its row or column holds too many, or when no tree stands beside it.
Nothing is given but the trees and the two strips of numbers, and there are always exactly as many tents as trees. One of the sentences above carries more than it looks: the tents and the trees pair off one to one. A tent may stand beside two or three trees and belong to only one of them, so “every tent has a tree beside it” is not the rule — a board can satisfy that and still be wrong. The crosses are your own notes of where no tent goes; only the tents are the answer. Every board has exactly one answer, and it can be reached without a single guess.
The counts alone
Four moves need no more than a look, and an 8 × 8 is made of them and nothing else. A line whose tents are all down: whatever is still open in it is crossed out. A line with exactly as much room left as it still wants: all of it is tents. A tree with one place left beside it: that place is its tent. And the eight cells round a tent, which no second tent may touch. Read them over and over — each one makes room for the next — and most boards fall to them alone.
Reading a whole line
When the counts stall, take one line and lay out every way its remaining tents could stand in it, two of them never side by side. Whatever all those readings agree on is settled: a cell holding a tent in every one of them is a tent, a cell holding one in none of them is crossed out. It is counting rather than guessing — the readings are all read, not tried one after another — and one line at a time is the whole move. A 10 × 10 needs it at least twice.
Tents and trees, paired off
The numbers know nothing about which tree a tent belongs to, and when they run out that is where the next move is. Tents and trees pair off one to one, so put the question to the wood instead of the lines. It has two forms. A cell no pairing can do without — withhold it and some tree is left with nowhere to go — holds a tent. And the other way round: a cell where a tent would cross out every place some tree had left is itself crossed out, because that tree would be left without one. With a single tree the first form is the glance move from the first chapter; what makes it an argument about the wood is two or three trees sharing the same places between them. A 12 × 12 needs the pairing at least twice.
No timer. Leave and come back — it’s saved.
Play today’s Tents and Trees