Loop Puzzle

How to play Loop Puzzle

Loop Puzzle is a pen-and-paper style logic puzzle played on a grid of dots. Your job is to join the dots with horizontal and vertical segments so that they form one single closed loop — a continuous ring that never crosses itself, never branches, and has no loose ends. Scattered around the grid are cells containing a small number from 0 to 3. Each number is a clue: it tells you exactly how many of that cell’s four sides are used by the loop. From nothing but these numbers you can deduce, square by square, where the loop must run and where it cannot go. Every puzzle here is computer-checked to have one and only one solution, so you never have to guess.

The goal

The goal is to draw a single unbroken loop along the grid edges that satisfies every numbered clue at once. When your loop is complete, three things must all be true: it is one continuous closed loop with no gaps, it never touches or crosses itself, and every number on the board matches the count of loop segments around it exactly. There is no clock that ends the game, but a timer and a mistake counter feed your score, so a clean, quick solve is rewarded.

The board and the numbers

The board is a lattice of dots arranged in rows and columns. Between any two neighbouring dots — up-and-down or left-and-right — lies a potential edge that the loop may or may not use. Each cell of the grid is bordered by exactly four such edges: top, bottom, left and right. A number written in a cell counts only the edges that touch that cell, so a 3 means three of its four sides carry the loop and one does not, while a 0 means the loop avoids that cell entirely. Tapping an edge cycles it through three states: a solid line (part of the loop), a small cross (marked as definitely empty), and blank (undecided). The crosses are memory aids for you — they are ignored when the puzzle is checked.

The rules

• Draw exactly one loop. Every edge you turn into a line becomes part of a single closed ring; when finished there must be one loop and nothing else — no separate second loop and no stray line sticking out.
• The loop never branches or crosses. At every dot the loop either passes straight through or turns a corner, which means each dot is touched by either zero lines or exactly two. A dot with one, three or four lines is illegal.
• Obey every number. A cell showing 0, 1, 2 or 3 must end up with exactly that many of its four edges drawn as lines. Cells with no number can have any count — they simply give no clue.
• A 0 means keep away. None of the four edges around a 0 may be used, so you can immediately cross all four of them off.
• You win the moment the drawn lines form one closed loop and every number is satisfied. The loop turns green and your time, mistakes and score are shown. Marking crosses is optional but helps you avoid errors.

Solving techniques

• Start with the 0s and 3s. Cross off all four edges of every 0. A 3 against the outside border, or two 3s in adjacent cells, forces several lines at once — these are the strongest opening moves.
• Use the corners of the grid. A clue in a corner cell has only two edges facing the outside; a 1 in a corner, for instance, tells you a lot about those two outer edges, because the loop must eventually turn there.
• Count what is left. If a cell needs two lines and two of its edges are already crossed off, the other two must be lines. If it needs one line and one edge is already a line, the remaining three must be crosses.
• Follow the loop’s ends. Because every dot has zero or two lines, a line arriving at a dot must leave it again. Trace each partial line until it is forced to turn, and cross off any edge that would create a third line at a dot.
• Avoid premature small loops. It is easy to accidentally close a little ring in one region while other clues are still unmet. Since the finished figure must be one single loop, never seal a loop until every number is accounted for.

Scoring and difficulty

Each solve is scored for the leaderboard with the formula score = 9000 − seconds − mistakes × 250, kept at a minimum of 1. In other words you begin with a notional 9000 points and lose one point for every second you take and 250 points for each mistake. A mistake is counted whenever a line you draw pushes a number over its target — for example adding a third line around a 2. Solve quickly and cleanly for the highest score. Difficulty sets the grid size and how many numbers are given: Easy is a 5×5 grid with generous clues, Medium a 7×7 grid, and Hard an 8×8 grid with the fewest clues, so more of the loop must be deduced. Scores are tracked separately for each size.

Frequently asked questions