How to play Tents and Trees

Trees are scattered through a forest. Pitch one tent for each tree. A tent must sit right beside its tree, and no two tents may touch. The numbers along the edges tell you how many tents belong in each line. With only three rules it is learned in moments, yet playing it, the “here or there?” reasoning turns out to be a real pleasure. What follows is the order to reason in.

The board sits in the middle. Green marks a tree, and the numbers along the left and top give the tents in that line.
The board sits in the middle. Green marks a tree, and the numbers along the left and top give the tents in that line.

First, look at the screen

The square grid is in the middle, with numbers along the left and the top.

  • The grid — green trees scattered about. Everything else is empty.
  • Numbers on the left — how many tents belong in that row.
  • Numbers on the top — how many tents belong in that column.
  • The top bar — tents still to pitch, time, and difficulty.
The board sits in the middle. Green marks a tree, and the numbers along the left and top give the tents in that line.
The board sits in the middle. Green marks a tree, and the numbers along the left and top give the tents in that line.

A number turns green when its line is complete and red when you have overshot it, so you can see at a glance what is finished.

This is what a finished board looks like

Pair every tree with a tent and it is done.

Tents are drawn as yellow triangles. Trees are the green trees.

Solved: every tree is paired with one yellow tent.
Solved: every tree is paired with one yellow tent.

There are always as many tents as trees. The edge numbers, added together, come to the same figure.

A tent goes right beside its tree

A tent must touch its tree along a row or a column — one of the four squares above, below, left or right.

Diagonals do not count. Touching only at a corner is not beside it.

A tent has to touch its tree across or down. Diagonally does not count.
A tent has to touch its tree across or down. Diagonally does not count.

So any square that touches no tree at all can never hold a tent. Cross those off first and the board narrows considerably.

No two tents may touch

Pitch a tent and no other tent may sit in the eight squares around it — not even one touching at a corner.

This is the most powerful rule in the game. Every tent you pitch settles eight squares at a stroke.

Pitch one tent and no other may sit in the eight squares around it — diagonals included.
Pitch one tent and no other may sit in the eight squares around it — diagonals included.

So the moment you pitch a tent, mark the ring around it as grass. Put it off and you will confuse yourself.

Reading the edge numbers

The numbers on the left and top are how many tents belong in that line. They are not the number of trees.

  • A line marked 0 holds no tents at all. It is grass from end to end.
  • When a line is complete its number turns green, and everything else in it is grass.
  • Overshoot the number and it turns red. Something is pitched wrongly.
The numbers along the left and top count tents in that line, not trees.
The numbers along the left and top count tents in that line, not trees.

Look for the 0s first. It is the easiest thing you can do the moment the board opens.

One tree, one tent

One tent per tree. A single tent cannot serve two trees, and two tents cannot both belong to one tree.

A tent sitting between two trees is fine — but it counts as the tent of one of them only. The other tree must have a tent of its own.

Each tree pairs with one tent. Getting the counts right is not enough on its own.
Each tree pairs with one tent. Getting the counts right is not enough on its own.

So having the right count is not enough. It is only truly finished when they can be paired off one to one, and the game checks that too.

How to tap

Each tap on an empty square cycles tent → grass → empty.

  • Once — pitch a tent.
  • Twice — grass, marked with a small dot. Your note that says “not here.”
  • Three times — empty again.
  • Press and hold to cycle backwards — grass comes first.
One tap for a tent, two for grass (a small dot), three to clear the square.
One tap for a tent, two for grass (a small dot), three to clear the square.

Tree squares do not change when tapped. Do not be sparing with grass marks. Crossing off what is not a tent is half this game.

First job — cross off what touches nothing

There is one thing to do the moment the board opens: mark as grass every square that touches no tree.

No tent can go there. This alone clears about half the board.

Every square that touches no tree marked as grass. The board has halved.
Every square that touches no tree marked as grass. The board has halved.

There is nothing to think about, so do it mechanically. The Hint starts here as well.

Next — clear the 0 lines

Find the lines marked 0 along the edges. They hold no tents, so they are grass from end to end.

Nothing to think about here either. And once those two jobs are done, so few empty squares remain that the real reasoning starts to show.

A line marked 0 is grass all the way across — the easiest thing to do the moment you open a board.
A line marked 0 is grass all the way across — the easiest thing to do the moment you open a board.

Even where it is not 0, once a line has as many tents as it needs, the rest of it is grass.

When the places equal the number needed

Now the real reasoning. Count the squares in a line where a tent could go.

If that count equals the number of tents the line needs, all of them are tents. There is nothing to choose.

  • Needs 3 and has 3 possible squares → all three are tents.
  • Needs 2 with 5 possible squares → you cannot tell yet. Look at another line.
  • When counting possible squares, leave out squares already grass and squares beside a tent.
When a line has exactly as many possible squares as tents needed, every one of them is a tent.
When a line has exactly as many possible squares as tents needed, every one of them is a tent.

This is the workhorse method. Sweep rows and columns alternately and settled squares come out one after another.

When a tree has only one place to go

You can reason from the trees as well. If a tree has only one square where a tent could go, that is its tent.

With three of its four neighbouring squares already grass, the remaining one is the answer.

If three of the four squares beside a tree are grass, the fourth is that tree's tent.
If three of the four squares beside a tree are grass, the fourth is that tree's tent.

Alternate between reasoning from lines and reasoning from trees. Stick to one and you stall quickly.

Beside a tent is grass, at once

Pitch a tent and the eight squares around it are settled as grass there and then — the four orthogonal and the four diagonal.

The knack is to mark them the instant you pitch. Put it off and you will reason over those squares again later.

  • One tent settles eight squares. A very large return.
  • Along an edge it is five squares; in a corner, three.
  • If a tree stands among those eight, leave it as it is — a tree is not a tent.
Place a tent and the eight squares around it become grass at once. Mark them as you go.
Place a tent and the eight squares around it become grass at once. Mark them as you go.

Because of this, the board narrows visibly with every tent. Which is why finding the certain tents first pays.

The hint gives you its reason

Press Hint at the top and it points out one square, says whether it is tent or grass, and tells you why.

  • Grass, because it touches no tree
  • Grass, because this line already has all its tents
  • Grass, because it is beside a tent
  • This line has exactly as many possible squares as tents needed
  • This tree has nowhere else to go
Hint says whether the next square is tent or grass — and why.
Hint says whether the next square is tent or grass — and why.

Those five reasons are all there are. Know them and you can solve any board dealt here.

You are told at once if it is wrong

Pitch against a rule and the square turns red.

  • When two tents touch — both squares turn red.
  • When a tent touches no tree
  • When a line overshoots its number — the edge number turns red as well.
Put two tents side by side and both squares turn red. You know the moment you place it.
Put two tents side by side and both squares turn red. You know the moment you place it.

Clear it as soon as it reddens. Reason on from it and everything else goes wrong.

Only boards with a single answer

Scatter trees and numbers carelessly and you get a board with several answers — where pitching correctly still gets you told you are wrong.

Here every board has its answers counted as it is built. If there is more than one, it is thrown away and built again.

Every board is checked for how many answers it has. Anything but one is thrown away and rebuilt.
Every board is checked for how many answers it has. Anything but one is thrown away and rebuilt.

A board someone sends you is counted again at your end.

You never have to guess

There is no need to solve by “let me pitch here and undo if it fails.”

Every board dealt here can be carried to the end with the five kinds of reasoning above and nothing else. That is checked before it is dealt.

A board that solves by reasoning alone, about half done — not one square was guessed.
A board that solves by reasoning alone, about half done — not one square was guessed.

So being stuck means there is a clue you have not seen. Sweep the lines and the trees again, alternately.

Reasoning with a gap between

A slightly more advanced technique. Once you have it, boards fall much faster.

Suppose a line has a run of squares where a tent could go. Since tents cannot touch, you can only place one every other square.

  • A run of five squares holds at most three tents.
  • A run of four holds at most two.
  • When the line needs exactly that maximum, where they go is settled.
  • Three tents in a run of five means the first, third and fifth. There is no other way.
Five squares in a row needing three tents can only be the first, third and fifth.
Five squares in a row needing three tents can only be the first, third and fifth.

It works the other way too. Two tents in a run of only three means the first and third, with grass in the middle.

Board size and difficulty

Choose the board size and difficulty from the menu.

  • 6 × 6 — five or six trees. Good for learning the rules.
  • 8 × 8 — around ten trees. The size that suits it best.
  • 10 × 10 — around twenty trees. A board takes a good while.
  • Easy, Normal, Hard — the more trees, the harder.
The menu sets the board size and the difficulty. Harder means more trees.
The menu sets the board size and the difficulty. Harder means more trees.

More trees means more tents, and more places where they get in each other’s way — which means more to reason about.

Sharing a board, and today’s puzzle

When you finish, press Copy this board’s link to send it to someone. Opening that link gives exactly the same board.

Today’s puzzle, below, is one set board per day. Everyone gets the same one, so you can compare times.

Solve it and a copy-link button appears. The other end checks again that the answer is unique.
Solve it and a copy-link button appears. The other end checks again that the answer is unique.

The receiving end counts the answers again too.

How to solve well

Work in this order and it usually falls. Top to bottom.

  • Cross off every square that touches no tree. The board halves.
  • Clear every 0 line. Up to here there is nothing to think about.
  • Count the possible squares in each line. If it equals the number needed, they are all tents.
  • Look from the trees as well. Find the tree with only one place to go.
  • Pitch a tent, then grass the eight squares around it at once. Put it off and you get muddled.
  • Sweep rows and columns alternately. Stick to one and you stall quickly.
  • Stuck? Hint. It gives the reason too, so next time you see it yourself.
Unreachable squares and zero lines cleared away, then the certain tents placed first.
Unreachable squares and zero lines cleared away, then the certain tents placed first.

Common mistakes

Boards that stall here nearly always come down to one of these four.

  • Treating a diagonal as beside — the most common. A tent must touch its tree along a row or column.
  • Not marking grass — leave the ruled-out squares unmarked and you re-examine the same place over and over.
  • Reading the edge numbers as tree counts — they are tent counts.
  • Pitching a tent and not clearing its ring — those eight squares are grass immediately. Mark them at once.
A tent pitched diagonally from a tree. It touches nothing, so it shows up red.
A tent pitched diagonally from a tree. It touches nothing, so it shows up red.

Clear a red square the moment you see one. Carry on with a conflict in place and finding where it began becomes very hard.

When you finish

Every tree paired with a tent, every line matching its number, no two tents touching — and it ends there.

The tents turn green and your time appears.

It ends when every tree has its tent and every line count is right. The tents turn green.
It ends when every tree has its tent and every line count is right. The tents turn green.

A best time is kept separately for each board size and difficulty.

Common questions

Can a tent go diagonally from its tree?

No. It must touch along a row or column — one of the four squares above, below, left or right.

What if two tents only touch at a corner?

That is not allowed either. No other tent may sit in the eight squares around a tent.

Are the edge numbers tree counts?

No, they are tent counts. The totals match, which makes it easy to confuse, but a line with three trees may hold only one tent.

Where do I start?

Mark as grass every square that touches no tree. Then the 0 lines. Those two alone halve the board.

Why mark grass at all?

Crossing off what is not a tent is half this game. Unmarked, you reason over the same square again and again.

Can one tree have two tents beside it?

No. It is one to one. A single tent between two trees is fine, though — it counts as the tent of one of them only.

I pitched them all and it will not finish.

The counts may be right while the pairing fails — one tree with two tents and another with none. Start from the red squares.

Could this board have several answers?

No. Every board has its answers counted before it is dealt, and any with more than one is discarded.

Is there ever a place where I must guess?

Never. Every board is built so that the five kinds of reasoning the hint uses carry you to the end.

If it is your first time
  • Start with the lines marked 0. That whole line is grass.
  • Any square that touches no tree is grass. Mark them all first and the board shrinks a lot.
  • If a line has exactly as many possible spots as tents needed, every one of them is a tent.
  • The moment you pitch a tent, the eight squares around it become grass. Mark them straight away.
  • Press Hint when you are stuck. It gives you the next square and the reason for it.