Bridge Links practice: rule out the crossing, then test the extra line.
Try an original eight-island challenge before revealing the reasoning. Use a forced crossing exclusion, test a tempting double, and compare your ten-edit answer with a complete lane ledger.
This challenge asks you to combine a local capacity argument with a geometric exclusion and a short contradiction. The positions resemble the first lesson’s layout, but it has a different set of clues. The six-island strategy board from lesson 2 has no crossing lanes; here a crossing is central to the solution.
Try the board before opening the answers. The goal is still to match every number in a single connected network. You are not racing a clock, and ten edits is a reproducible construction rather than a difficulty rating or a score you must beat.
Start with a blank crossing-practice board
Choose Practice this example beside the article, or Load advanced board in the game. Confirm the following eight clues and Edits 0. Each letter names an island; the digit is its required total of bridge lines. Dots are empty space. The diagram contains no bridges yet.
A3 . . B5 . . C3 . . . . . . . . . . . . . . D1 . . . . . E2 . . . . . . . . . . . . . . F1 . . G3 . . H2
The available lanes are AB, AD, BC, BG, CE, DE, DF, EH, FG and GH. BG is the vertical lane through the middle; DE is horizontal through the middle. They cross at empty space, so both cannot be occupied. A bridge may not pass through an island either: AC is blocked by B and AF by D.
Your worksheet: reasons before extra lines
- Which island needs more lines than its two outer lanes can supply? What does that force about the crossing lanes?
- Which corner must divide its total as a double on one side and a single on the other? Use the neighbour’s target as a capacity bound.
- After that deduction, find a low-number island with just one remaining neighbour.
- Can the central vertical lane be doubled? Follow the consequences through the lower-right corner and back to the top-right island.
- Finish, then check both the island totals and the complete network. Write down every lane count, including zeros.
Keep notes outside the game if you want a record of excluded lanes. The game stores your current lines and undo history in this tab, but it does not offer pencil marks or choose your next move. Check network counts the current groups; a partial check is not a guarantee that the branch can finish.
Two checkpoints without the complete answer
Use these checkpoints only after trying the worksheet. At the first checkpoint, B has three bridge lines, A has three and D has one. Edits is 4. At the second checkpoint, F also has its one line, G has two of its three, and Edits is 5. You should still be deciding whether a second central vertical line is possible.
If your numbers differ, do not add bridges merely to imitate a checkpoint total. Explain which lanes produced each total, or use Undo to revisit an unsupported decision. Retry this board removes every line and resets Edits to zero while keeping these exact eight clues.
Reveal the complete reasoning and ten-edit route
- Place one necessary BG line. B needs 5. AB and BC together supply at most 4, so BG must carry at least 1. Place one line without yet deciding whether it should be doubled. Once BG is occupied, DE must remain empty because the two lanes cross. Edits: 1.
- Use A’s restricted neighbour. A needs 3 from AB and AD. D’s target is only 1, so AD cannot exceed 1; AB cannot exceed 2. Both upper bounds must be reached: AB 2 and AD 1. D is now full, making DF 0 as well. Edits: 4. This is the first checkpoint.
- Connect F to G. F needs 1. DF is unavailable because D is full, leaving FG 1. G now has BG 1 + FG 1 = 2 of 3. Edits: 5. This is the second checkpoint.
- Test the extra BG line on paper. If BG were 2, then BG 2 + FG 1 would fill G, forcing GH 0. H would need EH 2. That would fill E, forcing CE 0. C needs 3 but could then receive lines only from BC, which carries at most 2. This is impossible. Indeed, B would already have AB 2 + BG 2, leaving only BC 1, so C could get just 1. Reject the hypothetical extra line; keep BG 1. This reasoning changes no bridge. Edits: 5.
- Finish the perimeter. B needs 2 more, so BC 2. C then needs CE 1. E needs EH 1, and H needs GH 1. G’s total is BG 1 + FG 1 + GH 1 = 3, so every number agrees. Edits: 10, with one connected group.
The full replay from empty in Cycle bridge count mode is BG, AB, AB, AD, FG, BC, BC, CE, EH, GH. Select the two named islands for each entry; after a pair the selection clears. The route uses ten bridge lines across eight occupied lanes. The two double connections are AB and BC.
AB 2 AD 1 BC 2 BG 1 CE 1 DE 0 DF 0 EH 1 FG 1 GH 1
Check the totals independently: A = 2 + 1 = 3; B = 2 + 2 + 1 = 5; C = 2 + 1 = 3; D = 1; E = 1 + 1 = 2; F = 1; G = 1 + 1 + 1 = 3; H = 1 + 1 = 2. DE is empty, so it cannot cross BG. Every island has a route to B: A and C connect directly, D through A, E through C, F through G, G directly, and H through G or E. This checks connection as well as arithmetic.
Make the wrong branch visible
For a separate experiment, return to the second checkpoint at Edits 5. Add the extra BG line, then add EH twice and BC once. Predict the final edit count, how many islands match, which island cannot finish, and how many groups are drawn. These changes are locally allowed; an accepted bridge is not an answer hint.
Reveal the nine-edit dead end and recovery
Edits becomes 9. Seven of eight island totals match, but C has only 1 of 3. There are two groups: E–H and A–B–C–D–F–G. E is full so CE cannot receive a line; B is full so BC cannot be increased. This drawing is not solved. To return exactly to checkpoint 2, choose Undo last edit four times, bringing Edits back to 5 and restoring BG 1, EH 0 and BC 0. You can then follow BC, BC, CE, EH and GH to finish at 10. Retry is another way to return to the same clues with no lines.
To remove a single or double connection directly, choose Clear connection before selecting its endpoints. Clearing an occupied lane counts as another edit rather than undoing history. Clearing an empty lane makes no edit. Retry and the lesson loaders restore Cycle bridge count, so check the selected action before following a replay.
Check the crossing refusal separately
Retry again for a one-edit test: draw DE once and then try BG. DE is locally legal even though it is incompatible with the proved solution. Predict what changes when BG is refused, and which connection must be removed before B can ever reach 5.
Reveal the crossing test answer
The proposed BG bridge is refused because it would cross DE. Edits stays 1 and the DE line remains. With BG blocked, AB and BC can together supply only 4 to B, below its target of 5. Thus DE was the unsupported choice. Choose Clear connection and select D then E to remove it; Edits becomes 2 and BG becomes available. Retry before replaying the ten-edit solution so the construction starts from zero.
What this challenge establishes
This original clue set was exhaustively checked for exactly one noncrossing connected solution. That check validates this board, not a difficulty label or a promise that one trick solves every bridge puzzle. The contradiction works because the earlier deductions are justified; carrying an arbitrary earlier guess into the argument would not prove the same result.
When finished, Undo reopens the last move and Retry keeps this challenge. Load beginner board and Load strategy board return to the earlier lessons; Load advanced board returns here. New puzzle leaves lesson practice and enters the finite seven-puzzle collection. A practice address reloads its matching clues after refresh, but the bridge drawing and history are not saved. No account, payment, or advertisement action is required.