Tents

Pitch one tent beside every tree — tents never touch, and the edge counts say how many camp in each row and column.

What it is

A grid scattered with trees. Every tree owns exactly one tent, orthogonally adjacent to it; tents never touch each other, not even diagonally; and the numbers along the edges count the tents in each row and column. Some counts may be omitted.

How to play

Zeros are free moves: grass the whole line. Cells beside no tree are grass too. Then work the counts — a line whose quota is met is done, and a line with exactly as many candidate cells as tents left fills them all. The endgame is usually a cornered tree with a single free spot.

Purpose

A newspaper and puzzle-app staple the catalogue lacked, and a structurally interesting one: the pairing rule (each tree ↔ its own tent) is a perfect matching, which the cell-level constraint model cannot express. The generator therefore proves it outright, which is a new kind of guarantee for the workspace.

History

Published as Zeltlager by Léon Balmaekers in 1989, and widely known through Simon Tatham’s puzzle collection and the World Puzzle Championship as Tents, or Tents and Trees.

This implementation

• Spec knobs: size (6–12), density (share of cells in tent–tree pairs), difficulty, cell, line.
• Generation: tents are placed first, none touching; a tree is attached beside each; the edge counts are then thinned away one at a time while the technique ladder still finishes the board at the requested ceiling.
• Solving: line counting and exact line enumeration (with the in-line separation rule folded in), tent–tent elimination, and the cornered-tree force.
• Guarantees: deterministic per seed; exactly one solution, proven by exhaustive count and checked to admit a perfect tree–tent matching; solvable by inference alone, rated by the hardest technique used.