FIXED PRACTICE BOARD
Bridges study 1
Solve at your own pace. Ask what follows from the position before applying the suggested move.
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Work from the current board
Use the route buttons beneath the diagram. They cycle unknown (0, 1 or 2) → exactly 1 → exactly 2 → 0 → at least 1 (1 or 2) → unknown. Dotted lines are possible routes, not established bridges.
Tab to any control and use Enter or Space.
Interactive help is separate from the written starting-board solution below.
What did this solve teach?
You met the complete win condition. Compare the written route below with your own moves. Identify one deduction you can explain without looking at the answer, and one place where a changed mark could invalidate the next conclusion.
Rules and proof limits
Join nearest visible islands horizontally or vertically with zero, one or two bridges per route. A bridge cannot pass through an island or cross another bridge between islands. Each island’s number counts individual bridges, and all islands must belong to one connected network.
A visible neighbour is only a possible route. Its remaining capacity and crossings may make it unusable. Correct island totals are insufficient without connectedness. Local capacity deductions need not finish every board; do not call a connection forced simply because it creates a tidy network.
Show the checked route from the starting position (6 steps)
This route starts from the original study position. It does not describe moves you made differently. Use “Explain a next step” for a deduction from your current marks.
- Island A needs 4 individual bridges. Its routes currently allow 0 to 4 in total. Holding the other routes within their limits restricts A–F to 2; B–A to 2. A domain “1 or 2” proves a connection but does not yet choose single or double.
- Island B needs 3 individual bridges. Its routes currently allow 2 to 4 in total. Holding the other routes within their limits restricts B–C to 1. A domain “1 or 2” proves a connection but does not yet choose single or double.
- Island C needs 3 individual bridges. Its routes currently allow 1 to 3 in total. Holding the other routes within their limits restricts C–D to 2. A domain “1 or 2” proves a connection but does not yet choose single or double.
- Island D needs 3 individual bridges. Its routes currently allow 2 to 4 in total. Holding the other routes within their limits restricts D–E to 1. A domain “1 or 2” proves a connection but does not yet choose single or double.
- Island E needs 2 individual bridges. Its routes currently allow 1 to 3 in total. Holding the other routes within their limits restricts G–E to 1. A domain “1 or 2” proves a connection but does not yet choose single or double.
- Island F needs 2 individual bridges. Its routes currently allow 2 to 4 in total. Holding the other routes within their limits restricts F–G to 0. A domain “1 or 2” proves a connection but does not yet choose single or double.
Final check
Every island has its exact bridge count, routes do not cross, and a graph traversal reaches every island.