dankpuzzles

join the islands, meet every number

Ligature, the bridges puzzle

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– Drag from island to island. Each number is its count of lines; all islands join up.

Loading today’s bridges puzzle…

Keyboard: arrows move between islands, Shift+arrow lays a line that way (a third press lifts both), Ctrl+Z undoes.

Your bridges puzzles

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Stars on the day: ★★★ 0 · ★★ 0

The streak counts bridges puzzles solved on their own day, one after another. A past puzzle keeps its stars but never changes the streak.

Past puzzles

Every earlier bridges puzzle, newest first; tap one to play it here with its own saved board. Past puzzles keep their stars but never change the streak.

    Ligature is the dankpuzzles bridges puzzle. In a printer’s type case a ligature is one piece of type that joins two letters with a stroke, as in fi or fl; here every line joins two islands. A new board every midnight UTC, the same for everyone: 7 by 7 on Monday and Tuesday, 8 by 8 on Wednesday and Thursday, 9 by 9 on Friday and Saturday, and on Sunday the week’s hardest 9 by 9.

    Stars: ★★★ for a solve without Hint or Check, ★★ with either. Hint shows the next step the site’s solver would take, with its reason in one sentence; Check says how many of your lines are wrong, not which. Undo and Restart are free. An island turns green when it has exactly its number of lines, and red when it has too many. Your progress stays in this browser only.

    Want something else? Today’s Typeslide is a sliding grid of letter tiles, the word ladder changes one letter at a time, the nonogram draws a picture from numbers and Quoin splits a grid into boxes. Or stay with bridges: More bridges makes practice boards in the size and level you pick.

    We count visits and plays anonymously. No cookies, no personal data.

    What we count

    Each visit adds one to a count for the page’s address, nothing more. The bridges puzzle adds six tallies, and today’s puzzles two more, each a fixed name with no puzzle number, no cookie and nothing about you or your board. One tally goes up by one when:

    • bridge-start you lay your first line on today’s puzzle (once a day per browser)
    • bridge-solve you finish today’s bridges puzzle (once a day per browser)
    • bridge-share you tap Share result after solving today’s puzzle
    • bridge-arrive you open the page from a shared result’s link (once per link per browser)
    • bridge-archive-solve you solve a past puzzle for the first time (once per puzzle per browser)
    • bridge-quick-solve you solve a practice board from More bridges (once per practice board)
    • set-done you have finished the last of today’s six puzzles (Typeslide, word ladder, nonogram, Quoin, this bridges puzzle and Lampblack) and this is the first page to notice it (once a day per browser)
    • reminder-add you tap Remind me every day under “All six done” and the calendar file is made (the time you picked is not sent)

    How to play the bridges puzzle

    A bridges puzzle is a square grid of water with numbered islands on it. You join the islands with straight lines. Ligature is this site’s daily one, the same for everyone and new at midnight UTC.

    The rules

    1. The number is the count of lines. A 1 has one line, a 4 has four: say a double to one neighbour and a double to another, or a double and two singles.
    2. Straight lines, nearest island only. A line runs across or down to the next island in that row or column. It never bends and never jumps over an island.
    3. At most two lines between a pair. One line or a double line, never three.
    4. No crossings. A line across and a line down may not cross in the water.
    5. One network. When you are done, you can walk from any island to any other along the lines. Two islands that only join each other do not count.
    6. Laying lines. Drag from one island to its neighbour to lay a line; drag again for a double. Tap a line to cycle it single → double → none. A line that would cross another, or pass over an island, is refused with a short note.
    7. You never have to guess. Every board was checked by this site’s solver to have exactly one answer that reasoning alone reaches. Hint shows its next step; Check counts your wrong lines without naming them. Either one caps the day at two stars.

    Ways in

    • Full count. An island whose number equals everything its neighbours can still take must take all of it. A 4 in a corner sees two islands at most: a double to each. A 1 that sees only one island joins it.
    • Forced share. A 3 with two neighbours has at least one line to each: two lines to one side still leave one for the other. A 5 with three neighbours has at least one to each; a 7 with four has at least one to each.
    • Do not close off a group. Two 1s may never join each other, two 2s never take a double between them: the pair would be finished and cut off from the rest.
    • The only way out. A group of joined islands that still needs lines and has one neighbour left to reach must use it.
    • Sunday’s what-if. Suppose a pair holds no line at all, follow the counting for a few steps, and if an island can no longer reach its number or the network can no longer join up, the pair must hold a line.

    Worked example: a 7 by 7

    1 2 3 3 2 3 1 3 4 3 1
    1. The 1 in row 1 sees only one island, the 2 at the right end of its row (nothing sits below it): one line. That 2 needs one more and sees only the 3 below it in row 3: one line. That 3 needs two more and sees only the 4 in row 5: a double.
    2. The bottom-left 3 sees the 3 above it in row 2 and the 1 in the bottom-right corner. A 1 takes one line at most, so 3 = 2 + 1: a double up and a single across. The 3 in row 2 then needs one more and sees only the 3 to its right: one line.
    3. The 4 in row 5 has two from above, and the 1 below it is already full, so its other two go left: a double to the 3 in row 5. That 3 is now one short.
    4. The 3 in row 2, column 3 has one line and needs two more, from the 2 on its right (two at most) and the 1 below it (one at most). Without the 2 it could reach only 2, so it has at least one line to the 2.
    5. Could that be a double? Then the 3 and the 2 would both be full, and so would the islands already joined to them (the two left-hand 3s and the corner 1): five islands finished and cut off from the other six. So it is a single, and the 3 takes its last line down to the 1. The 2 needs one more and sees only the 3 in row 5 below it: one line. Ten steps, every island joined, no guess.

    This board was made for this guide by the same generator and checks as the dailies (one answer, reached without guessing) and is never a daily puzzle. Every Friday and Saturday board, and many midweek ones, also need the cut-off and only-way-out ideas above; every Sunday board needs the what-if.

    Where the puzzles come from

    Every board is made and checked by this site’s own code, a year ahead. A generator grows a random network of islands joined by straight lines (single or double, never crossing, no two islands side by side), closes a few loops, and writes each island’s count of lines as its number. Then the site’s solver tries to finish it the way a person would, using only four kinds of reasoning (full count, forced share, the cut-off and only-way-out rules, and a one-step what-if). A board is kept only if the solver finishes it and a separate exhaustive count finds exactly one answer.

    The year from 24 October 2026 holds 365 boards: 105 easy 7 × 7 with about 11 islands, 104 middle 8 × 8 with about 15, 104 hard 9 × 9 and 52 Sunday 9 × 9 with about 20, none the same as another even turned or mirrored. Most easy boards fall to the full-count rule alone in about eight steps; every Sunday board needs the what-if. Honest limits: the solver knows four rules and no deeper look-ahead, so the levels are its view of difficulty, not a tester’s; 59 of the 104 midweek boards need nothing beyond the forced-share rule, so Wednesday is often a step up in size more than in trickiness.

    Made with AI tools.