Cranes.

Cranes rest on sandbanks. Join the sandbanks with straight walkways so that every sandbank has as many walkways as its number, at most two between the same pair, no crossings, and every sandbank can be reached from every other.

A walkway runs straight across the water, up and down or left and right, and only between two sandbanks that stand in line with nothing in between. Two walkways may run side by side between the same pair, and that counts as two for both of their numbers.

The number on a sandbank is the whole truth about it: when it says four, exactly four walkways leave it, no more and no fewer. When the last number is right and the sandbanks hang together in one piece, the water is finished and the game notices by itself.

Tap or click the water between two sandbanks that stand in line: once lays one walkway, twice lays two, a third time takes them away. You can also drag from one sandbank straight to another. Shift and a tap, or the right button, notes a pair as never joined; that note is only for you and is never checked. Nothing lights up while you play: finding a mistake is part of the puzzle.

Check first tells you only how many walkways are wrong and roughly where. Press it again and it shows which. Hint names the rule and the place, and the second press builds that one step for you. If something on the board is already wrong, the hint points there first. Hints and checks are free and counted, and shown when you finish. Clear empties the water; the clock keeps running and one Undo brings everything back.

Keyboard: arrows walk from sandbank to sandbank, Ctrl plus arrow lays a walkway that way and pressing again makes it two and then none, Shift plus arrow notes that pair as never joined, Enter or Space works on the direction you used last, X notes it, Delete clears it, U or Ctrl+Z undo, R or Ctrl+R redo, P pauses.

The clock runs from your first walkway to the last one and pauses when you leave the tab or sit still for a minute, which also hides the water. Your progress, time, history and day streak stay in this browser, and in your account when you are signed in, so you can continue on another device.

A water finished with no hint and no check counts as clean and the week strip gives it a second ring. Only the water of the day builds the streak, and after five days in a row one missed day is forgiven, at most twice in a month. When you finish, Share copies one line with the date, your time and how much help you took. It never copies the water or your walkways, so nothing is spoiled for anyone.

Monday and Tuesday are easy (a seven by seven water with ten to twelve sandbanks), Wednesday and Thursday medium (nine by nine, sixteen to twenty), Friday and Saturday hard (eleven by eleven, twenty four to twenty eight) and Sunday is the challenge: thirteen by thirteen with thirty two to thirty eight. The week strip under the water takes you to the other days; the archive goes back a year, and the practice sets have eight waters of each level with no date attached.

Difficulty is measured, not guessed. Every water is solved by a program that only knows named rules, in three layers: what a single number allows on its own, the patterns between two numbers, and the hard ones, where a count is tried out for one step and ruled out because it ends in a contradiction or cuts a group of sandbanks off from the rest. Easy and Medium never need that third layer; Sunday leans on it the most.

No water, not even a Monday, can be beaten by tapping every stretch once. At least three in ten of the pairs you can see are there to be left alone, and at least a quarter of the walkways that do belong are doubles, so the shape of the answer never matches the shape of what is in front of you. On Friday, Saturday and Sunday there is always a crossing to steer around as well.

Start at the edges and the corners. A sandbank in a corner reaches only two others, so a 4 there means two walkways to each, and a 3 means at least one to each.

A 1 with a single neighbour, or a 2 with a single neighbour, has nowhere else to go. So does any sandbank whose neighbours have exactly as much room left as its number still needs.

Two sandbanks with a 1 never join to each other, and two with a 2 never join twice: the pair would be finished and cut off from the rest of the water, and every sandbank has to be reachable from every other.

When a walkway crosses the line between two other sandbanks, that pair is closed for good. Note it and move on; those notes are what turn a crowded middle into a chain of forced steps.