TECHNIQUE 2 OF 4
Tree neighbours: necessary does not mean sufficient
List the squares a tree could actually use, and distinguish them from squares that only look nearby. Keep the eventual one-to-one matching in mind when trees share candidates.
The rule
A tent must be directly above, below, left or right of some tree; a non-tree square with no such neighbour is grass. If a tree has no existing adjacent tent and exactly one remaining legal neighbouring square in a consistent position, that square must contain a tent. If tents or candidates are shared between trees, check whether a complete one-to-one assignment is still possible.
A common mistake
Counting diagonal tree neighbours allows illegal tents. Greedily assigning any nearby tent to a tree can also strand a second tree that has no alternative.
TRY IT 1 · tents-adjacency-1
| C11 | C21 | C30 | C41 | C51 | C62 | |
|---|---|---|---|---|---|---|
| R11 | ||||||
| R21 | ||||||
| R30 | ||||||
| R42 | ||||||
| R50 | ||||||
| R62 |
What can you justify?
Use the tree neighbours technique. What does it prove about R1C1? Treat the displayed starting marks as established facts.
Written explanation
R1C1, R1C5, R1C6, R2C1, R2C2, R2C4, R2C6, R3C1, R3C3, R5C1, R6C1, R6C2, R6C3 have no tree directly above, below, left or right. A diagonal tree is not sufficient, so these squares are grass.
TRY IT 2 · tents-adjacency-2
| C12 | C21 | C32 | C41 | C51 | C60 | |
|---|---|---|---|---|---|---|
| R12 | ||||||
| R21 | ||||||
| R31 | ||||||
| R41 | ||||||
| R50 | ||||||
| R62 |
What can you justify?
Use the tree neighbours technique. What does it prove about R1C4? Treat the displayed starting marks as established facts.
Written explanation
R1C4, R1C6, R3C1, R3C4, R3C6, R4C4, R4C5, R4C6, R5C4, R5C5, R5C6, R6C1, R6C5, R6C6 have no tree directly above, below, left or right. A diagonal tree is not sufficient, so these squares are grass.
A remaining square is not a second tent requirement
A tree at R3C3 already has an established tent at R2C3. R3C2 and R3C4 are grass; R4C3 is unknown. No full tree assignment has been specified.
The tempting move
Place another tent at R4C3 because it is the tree's only remaining unknown neighbour.
Why it fails
The tree already has an adjacent tent that may serve it. Counting only unknown neighbours ignores that existing possibility. The rule does not require an additional tent whenever a tree has one unfilled candidate.
What is actually justified
Adjacency alone does not force R4C3. Determine the relevant tree matching and use the row and column totals. R4C3 might be needed for another tree or might be grass; the stated facts do not settle it.
Transfer the idea
Tree A has only tent X beside it. Tree B is beside tents X and Y. Both tents must belong to exactly one of these trees. Which pairing is possible?
Check your reasoning
A must take X, its only adjacent tent, and B must take Y. Assigning X to B would leave A unmatched. The shared adjacency does not mean X can serve both trees.