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Bridges

Join numbered islands with straight bridges, one or two per pair, never crossing, all in one group. Small boards first; every puzzle has one solution.

  • Logic
  • Untimed
  • 12 levels

How it plays

Each circled number is an island and says how many bridges touch it. Bridges run straight across (─, or ═ for two) or straight down (│, or ‖ for two) between two islands, never cross each other, and together join every island into one group. Fill each open cell with its bridge, or · where there is none.

Start where there is no choice: an island with one neighbour, a 4 in a corner, an 8 in the middle. Then count, for each island, what it still needs against what it can still reach, and keep in mind that no group may close itself off.

Boards grow from 5×5 with four islands to 11×11 with twenty. Every board is built from a solution and solved again from the numbers alone; if a second solution exists it is redrawn, or a bridge is drawn in for you, until exactly one remains.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This practises constraint counting and case-splitting on these puzzles. It is practice at bridges, not a measured gain in reasoning elsewhere.

Learn

How to get better at bridges: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. For each island, find the islands it can see: the nearest one in each straight direction, with only open cells between. An island sees at most four, and a corner island at most two.
  2. Start with the islands that have no choice — a number that fills every bridge it could take, or an island with a single neighbour. Draw those bridges first.
  3. Every bridge you draw cuts the board: no other bridge may cross it, so islands on either side may lose a neighbour. Recount what each island near the new bridge can still see.
  4. Keep a running “still needs” for each island — its number minus the bridges already touching it — and compare it with what it can still reach. When the two are equal, every remaining bridge is forced.
  5. When every number is met, fill each open cell left over with ·. Those cells are part of the answer too.

Techniques and tricks

  • Full house

    An island whose number is twice the count of islands it can see must take a double bridge to every one of them.

    e.g. A ④ in a corner sees two islands, so it is ═ to one and ‖ to the other

  • One short of full

    An island whose number is one less than twice its neighbours must take at least one bridge to each — a double to one and none to another would leave it short.

    e.g. A ③ seeing two islands: with nothing to one side, the other could give at most 2, which is short of 3 — so each side gets at least one

  • The lone neighbour

    An island that can see only one other island sends all its bridges there. Watch for this after a crossing bridge has cut off a neighbour.

  • No closed pairs

    Everything must end as one group. Two ①s joined to each other are finished and cut off, so a ① never bridges to a ①; nor does a ② take a double to another ②.

    e.g. A ① sees a ① and a ③: it must bridge to the ③

  • Count the bridges

    The total number of bridges is half the sum of all the numbers, since each bridge touches two islands. A double counts as two. A quick check when the board looks finished.

    e.g. Islands ③ ② ② ①: (3 + 2 + 2 + 1) ÷ 2 = 4 bridges

  • Reach versus need

    Add up the most each neighbour could still take — two, or less if that neighbour needs less. If that sum equals what the island still needs, take the most on every side.

    e.g. A ⑤ sees a ① and two islands that can each take two: 1 + 2 + 2 = 5, so all three bridges are at their most

As the levels climb

  • The ladder starts on a 5×5 with four islands and adds an island or a size at each step: 5×5 with five, 6×6 with six and seven, 7×7 with eight and ten, 8×8 with eleven and thirteen.
  • Then 9×9 with fourteen and sixteen, 10×10 with eighteen and 11×11 with twenty. A draw can come out with an island or two fewer than its rung’s count. With more islands, more of them stand in each other’s way, so each bridge you draw cuts off more neighbours: recount after every one.
  • On small boards Full house and The lone neighbour finish most puzzles. On the big ones you will reach a point where nothing is forced by counts alone; then No closed pairs and the one-group rule are what break the deadlock.
  • When a board had two solutions from its numbers alone, one pair’s bridges are drawn in for you. Treat a drawn-in bridge as a strong clue: it is there because the board needs it.
  • The clock is off unless you turn on Time pressure; then you get 60 seconds plus 6 seconds for each open cell. Marking the · cells takes time on an 11×11, so leave room for it.

Traps to avoid

  • Crossing a bridge. A ─ and a │ may never meet in one cell. Before you draw a long bridge, check that no bridge already runs through its path.
  • The wrong stroke. ─ and ═ go across, │ and ‖ go down; a down bridge drawn with ─ is marked wrong cell by cell. Pick the symbol by direction, then by one or two.
  • Closing off a group. Every number can be met and the board still be wrong because two islands, or a small cluster, are joined only to each other. Before finishing, trace that every island links to every other.
  • Leaving cells blank. Each open cell with no bridge must be marked ·, and each one is scored. A board with every bridge right and empty cells is not complete.

How to practise

  • Set “Largest board” to 7 and play until Full house and One short of full jump out at you, then raise it a size at a time to 11.
  • Before drawing anything, say each island’s neighbour count to yourself. Doing this on every board is what makes the forced moves visible at a glance.
  • Leave Time pressure off while you learn the counting, and move to Relaxed when the 9×9 boards come out right first time.
  • When you get a board wrong, read the “first step” in the working and find that island before you check the rest — it shows the move you overlooked.

Levels

It is untimed unless you turn the clock on. There are 12 levels with the default settings, and the counter stops at the real top. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More logic

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