TECHNIQUE 4 OF 4
Remaining counts: finish a line in either direction
A nearly completed row can tell you either where tents must go or where they cannot go. Count the remaining requirement and the remaining legal locations separately.
The rule
Subtract the established tents from the line's clue. If nothing remains to be placed, mark every other undecided non-tree square in the line as grass. If the remaining requirement equals the number of legal candidate squares, all those candidates must be tents. Their spacing and tree matching must still be compatible; conflicting forced placements reveal an inconsistent earlier state or candidate list.
A common mistake
Counting trees as available tent spaces inflates capacity. Treating two touching candidates as usable together also produces a false count deduction.
TRY IT 1 · tents-counts-1
| C11 | C21 | C30 | C41 | C51 | C62 | |
|---|---|---|---|---|---|---|
| R11 | ||||||
| R21 | ||||||
| R30 | ||||||
| R42 | ||||||
| R50 | ||||||
| R62 |
What can you justify?
Use the remaining counts technique. What does it prove about R2C5? Treat the displayed starting marks as established facts.
Written explanation
Row 2 needs 1 tents and already has 0. Its 1 remaining candidate square must all be tents because every candidate is needed.
TRY IT 2 · tents-counts-2
| C12 | C21 | C32 | C41 | C51 | C60 | |
|---|---|---|---|---|---|---|
| R12 | ||||||
| R21 | ||||||
| R31 | ||||||
| R41 | ||||||
| R50 | ||||||
| R62 |
What can you justify?
Use the remaining counts technique. What does it prove about R1C3? Treat the displayed starting marks as established facts.
Written explanation
Row 1 needs 2 tents and already has 0. Its 2 remaining candidate squares must all be tents because every candidate is needed.
Enough squares is not enough compatible capacity
Row 4 requires two tents and currently contains none. Its only candidate squares are R4C2 and R4C3; assume each has an adjacent tree, while all other non-tree squares in the row are grass.
The tempting move
Place tents in both candidates because the row needs two and exactly two squares remain.
Why it fails
The candidates touch along a side, so they cannot both be tents. The row requirement and the current exclusions cannot all be satisfied in this state.
What is actually justified
Report a contradiction and revisit earlier marks or the candidate analysis. The count rule does not grant an exception to spacing. The displayed facts do not identify which earlier decision caused the problem.
Transfer the idea
A row requires three tents and already has one established tent. Exactly two legal candidate squares remain; they do not touch each other or the existing tent and can be assigned to the remaining trees. What follows? What would follow if there were three candidates instead?
Check your reasoning
With two candidates and two tents still required, both candidates are tents. With three candidates, the count alone says that two are tents but does not identify which two; use columns, spacing or tree matching to narrow the choice.