TECHNIQUE 3 OF 4
Tent spacing: check the corners too
Placing one tent often rules out several nearby squares. Those exclusions can be more useful than the placed tent itself when you return to the row and column totals.
The rule
No other tent may occupy any of the eight surrounding squares: above, below, left, right or diagonal. Mark surrounding undecided non-tree squares as grass. Keep tree squares unchanged. Apply this only to a tent whose placement is established, because an unsupported tent would spread unsupported exclusions.
A common mistake
Checking side contact but missing diagonal contact admits an invalid pair. Conversely, tents with one full square between them do not touch merely because they share a row or column.
TRY IT 1 · tents-spacing-1
| C11 | C21 | C30 | C41 | C51 | C62 | |
|---|---|---|---|---|---|---|
| R11 | ||||||
| R21 | ||||||
| R30 | ||||||
| R42 | ||||||
| R50 | ||||||
| R62 |
What can you justify?
Use the tent spacing technique. What does it prove about R1C4? Treat the displayed starting marks as established facts.
Written explanation
The tent at R2C5 excludes all touching squares, including diagonals. Mark R1C4 as grass.
TRY IT 2 · tents-spacing-2
| C12 | C21 | C32 | C41 | C51 | C60 | |
|---|---|---|---|---|---|---|
| R12 | ||||||
| R21 | ||||||
| R31 | ||||||
| R41 | ||||||
| R50 | ||||||
| R62 |
What can you justify?
Use the tent spacing technique. What does it prove about R2C2? Treat the displayed starting marks as established facts.
Written explanation
The tent at R1C3 excludes all touching squares, including diagonals. Mark R2C2, R2C4 as grass.
Two available trees do not excuse diagonal tents
A tent is established at R2C2. R3C3 is an unknown non-tree square beside a tree at R3C4.
The tempting move
Place a tent at R3C3 because it has a tree immediately to its right.
Why it fails
R3C3 touches the established tent at R2C2 diagonally. Orthogonal adjacency to a tree satisfies one requirement but cannot override the tent separation rule.
What is actually justified
Mark R3C3 as grass. The tree at R3C4 must obtain its tent elsewhere in any valid completion.
Transfer the idea
A tent is at R3C3. Consider R2C2 and R3C5. Which is forbidden by this tent's spacing rule, and is the other automatically a valid tent location?
Check your reasoning
R2C2 is forbidden because it touches R3C3 diagonally. R3C5 is two columns away and is not forbidden by this tent alone. It still needs an adjacent tree, room in its row and column counts, and separation from any other tents.