Tents and Trees Puzzle
Pitch one tent beside every tree with no two tents touching. A board holds at most a quarter of its squares — and a 6x6 holds no more than a 5x5.
Every tree gets one tent, directly beside it — never diagonally. Tents may not touch each other at all, corners included. The numbers say how many tents belong in each row and column. Click once for a tent, again for grass.
A board holds at most ⌈n/2⌉² tents — a quarter of it
Tents may not touch, not even at a corner, and that one rule caps how many can ever fit. The cap is exact, and it is checked here against a search over every legal row pattern from 1×1 to 14×14 — a search that knows nothing about the formula — with no mismatches at any size.
| Board | Squares | Most tents that fit | Share of the grid |
|---|---|---|---|
| 3 × 3 | 9 | 4 | 44.4% |
| 4 × 4 | 16 | 4 | 25.0% |
| 5 × 5 | 25 | 9 | 36.0% |
| 6 × 6 | 36 | 9 | 25.0% |
| 7 × 7 | 49 | 16 | 32.7% |
| 8 × 8 | 64 | 16 | 25.0% |
| 9 × 9 | 81 | 25 | 30.9% |
| 10 × 10 | 100 | 25 | 25.0% |
| 11 × 11 | 121 | 36 | 29.8% |
| 12 × 12 | 144 | 36 | 25.0% |
On every even board it works out at exactly a quarter of the squares — 16 of 64 on an 8×8, 100 of 400 on a 20×20, a flat 25% however large it gets. So no puzzle can ever ask for more trees than a quarter of its grid, and one that feels crowded is closer to that ceiling than it looks.
And a 6×6 board holds no more tents than a 5×5
The formula rounds up, so it takes two extra rows to make room for another tent. A 3×3 and a 4×4 both hold four. A 5×5 and a 6×6 both hold nine. A 7×7 and an 8×8 both hold sixteen.
A 6×6 grid has eleven more squares than a 5×5 and room for exactly the same nine tents, because the extra rank and file land in the gaps the spacing rule already demanded. Growing the board by one in each direction buys you nothing whatever.
Which is also why the odd boards are the dense ones. Nine tents on twenty-five squares is 36% of a 5×5, against a flat 25% on every even board. If you want a crowded puzzle, ask for an odd grid.
Notes
- Tents pair with trees one-to-one. A tent beside two trees still only serves one of them, so counting neighbours is not enough — the puzzle needs a genuine matching, which is what the checker tests.
- Trees may touch each other. Only tents are kept apart, which is what makes clumps of trees the interesting part of a grid.
- Diagonal contact counts. Two tents cornering each other is illegal, and that is the rule doing all the work in the packing limit above.
- Every puzzle here has exactly one answer, confirmed by counting solutions rather than by trusting the generator that made it.
How to use
- Give every tree exactly one tent, directly beside it and never diagonally.
- Keep tents apart — they may not touch even at a corner.
- Match the numbers beside each row and column.
- Click once for a tent and again to mark grass.
Frequently asked questions
What are the rules of Tents and Trees?
Every tree gets exactly one tent placed directly beside it, horizontally or vertically but never diagonally. No two tents may touch each other at all, corners included. The numbers beside each row and column say how many tents belong there.
How many tents can fit on a grid?
At most the ceiling of half the width, squared. On an eight by eight that is sixteen, on a twenty by twenty it is a hundred. The limit is checked here against a search over every legal row pattern up to fourteen by fourteen, which knows nothing about the formula and agrees at every size.
Why is a quarter of the board the limit?
Because tents cannot touch, so each one effectively claims a two by two area. On any even board that works out at exactly a quarter of the squares, however large it gets, which caps how many trees a puzzle can ever contain.
Does a bigger board always hold more tents?
No. The formula rounds up, so it takes two extra rows to make room for another tent. A six by six board has eleven more squares than a five by five and room for exactly the same nine tents, because the extra rank and file land in the gaps the spacing rule already demanded.
Which board sizes give the densest puzzles?
Odd ones. Nine tents on twenty-five squares is thirty-six per cent of a five by five, against a flat twenty-five per cent on every even board. If you want a crowded puzzle, ask for an odd grid.
Can two trees share a tent?
No. The pairing is one to one, so a tent standing between two trees still only serves one of them. Counting neighbouring tents is not enough to check an answer — it needs a genuine matching, which is what this page tests.
Can trees touch each other?
Yes, freely. Only the tents are kept apart, which is why clumps of trees are the interesting part of a grid — several trees competing for the few squares that can hold a tent.
Does every puzzle have exactly one answer?
Yes. Each generated puzzle is checked by counting its solutions and thrown away unless there is exactly one, rather than trusting the generator that produced it.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.