TECHNIQUE 2 OF 4
Remaining capacity: subtract at both ends
Once bridges are placed, the opening neighbour count is no longer enough. Track what the island still needs and what each neighbouring island can still accept.
The rule
Subtract placed individual bridges from an island's clue. Limit each remaining connection by the two-bridge maximum and the remaining capacities of both endpoints. A satisfied neighbouring island cannot accept an additional bridge. If the required total exhausts the remaining capacities, those contributions are forced.
A common mistake
Treating every visible neighbour as two free spaces ignores bridges already attached to that neighbour. Also, a double connection contributes two, not one, to each endpoint.
TRY IT 1 · bridges-remaining-1
What can you justify?
What range can the displayed remaining deduction establish for route E–A?
Written explanation
Island A needs 2 individual bridges. Its routes currently allow 1 to 4 in total. Holding the other routes within their limits restricts E–A to 0 or 1. A domain “1 or 2” proves a connection but does not yet choose single or double.
TRY IT 2 · bridges-remaining-2
What can you justify?
What range can the displayed remaining deduction establish for route G–H?
Written explanation
Island H needs 2 individual bridges. Its routes currently allow 1 to 2 in total. Holding the other routes within their limits restricts G–H to 2. A domain “1 or 2” proves a connection but does not yet choose single or double.
A visible neighbour can already be full
A needs one additional bridge and has two geometric neighbours B and C. B's clue is already completely satisfied by established bridges to other islands. C has capacity for one more, and A–C is an available route.
The tempting move
Keep both A–B and A–C as equally available ways to finish A.
Why it fails
An additional bridge to B would exceed B's clue. Geometric visibility does not create remaining capacity at the endpoint.
What is actually justified
A's additional bridge must go to C, assuming the stated position is consistent. A–B cannot receive a new bridge.
Transfer the idea
Island A still needs three bridges. Its only unfinished routes lead to B and C. B can accept at most one more bridge and C at most two. How many additional bridges must each route carry?
Check your reasoning
A–B must receive one additional bridge and A–C two. Their combined remaining capacity is exactly three, so neither route can supply less. This assumes the stated routes are legal and their existing counts leave that much room under the per-route limit.