How to play Number Loop

Number Loop is a puzzle drawn on a grid of dots. Some of the squares between the dots hold a number from 0 to 3. Your job is to draw a single closed loop by joining neighbouring dots with straight lines, so that every number tells exactly how many of its square's four sides the loop runs along. A 3 is wrapped on three sides, a 1 is touched on just one, and a 0 is never touched at all. Squares without a number can have any number of sides on the loop.

The loop never branches, never crosses itself and never touches itself at a dot: it is one clean line that comes back to where it started. Puzzles like this are also known as loop puzzles, Fences or Loop the Loop. On skill.games every puzzle is new: it is made by the game when you start, and checked before you see it. Each one has exactly one solution, and you can always reach it by reasoning, step by step. You never have to guess.

How to play on skill.games

When you open the game, the settings popup appears. Pick a difficulty - Easy, Normal, Hard or Crazy - and how mistakes are handled (see "Mistakes" below), then press PLAY. Your choices are remembered for next time. A new puzzle takes a moment to make.

• Drawing a line: tap the gap between two dots. The first tap draws a line there, the second puts a small cross (a note that the loop does not go there), the third clears it again. On a computer, click.
• Drawing with your finger: put your finger near a dot and drag along the dots. Every gap you pass over gets a line, so a long stretch of the loop takes one stroke, corners included. If you drag back along the way you came, the lines you leave are taken back.
• Erasing by dragging: a drag that starts along an existing line erases lines instead of drawing them.
• Crosses on a computer: right-click a gap to put a cross there, or to remove one.
• Undo: the UNDO button takes back your last tap or drag, as many times as you like. It's free. On a keyboard, Z does the same.

Numbers turn grey when their square has exactly as many lines as they ask for (a 0 turns grey once you have crossed all four of its sides). The clock at the top shows your time.

The menu button in the top-left corner pauses the game and the clock, starts a new game or switches the sound on or off. The "?" button in the top-right corner opens this guide. The game is saved as you play, so if you close the page you can press CONTINUE and carry on with the same puzzle.

Rules

The loop. Draw lines between neighbouring dots, across or down - never diagonally. Together they must form one single closed loop. Every dot is either not on the loop at all, or has exactly two lines meeting at it. A dot with three or four lines would be a branch or a crossing, and a dot with one line is a loose end.

The numbers. A number counts how many of its square's four sides are part of the loop. Every number on the board must be exact when the loop is finished. Blank squares have no rule.

The goal. The puzzle is solved the moment your lines are exactly the loop. Crosses don't matter: you never need to mark the gaps the loop doesn't use.

Rule breaks are shown. While you draw, the game points out anything that cannot be part of a solution: a number with too many lines around it, or with so many crosses that it can no longer be reached, turns red; a dot with three or more lines turns red; and a closed loop that leaves other lines outside it is drawn red, because the answer is a single loop.

Mistakes. In the settings you choose one of two ways to play:

• Unlimited: your lines are not checked against the answer while you draw - only the rule breaks above are shown. You find out about a wrong line when the puzzle stops making sense.
• 3 lives: every line and cross is checked as you draw it. A line where the loop doesn't go becomes a red cross; a cross where it does go becomes a red line. Either way that gap is locked, costs one life, and a drag stops there. The third mistake ends the game. Undo never gives a life back.

A puzzle you leave unfinished for a new one counts as a loss in your statistics.

Solving techniques

Every puzzle here can be finished with the techniques below. The higher levels need the later ones.

• Zeros first. A 0 has no line on any side. Cross all four sides straight away; it often settles its neighbours.
• Counting a square. When a number already has that many lines, cross its other sides. When it has as many open sides as it still needs, all of them are lines. A 3 with one side crossed has lines on the other three.
• Counting a dot. A dot with two lines is finished: cross its other gaps. A dot with one line and only one open gap must continue through that gap. A dot whose other gaps are all crossed can't take a line in the last one either, because the loop would stop there.
• Corners. A 3 in a corner of the board has lines on both of its outer sides; a 1 in a corner has crosses on both. More generally, look at a number's four corner dots: if a line runs into a 1's corner, the 1's two sides away from that corner are crossed, and a line running into a 3's corner means the 3's two far sides are lines.
• Pairs of numbers. Two 3s side by side always have lines on the side they share and on both outer sides opposite it. Two 3s touching at a corner have lines on their two far corners. A 3 next to a 1, a 2 next to a 3 and similar pairs give their own small rules; look at two numbers together when each alone gives nothing.
• Don't close too early. If one more line would close a loop while other lines are still left outside it, that gap gets a cross. This is often the key to the last part of a puzzle.
• Parity. Going along any row of squares from the left edge to the right edge, you cross the loop an even number of times: every time you go in, you must come out. So the lines on the vertical gaps of a row (and likewise the horizontal gaps of a column) add up to an even number. When only one gap of a row is still open, the count decides it.
• Inside and outside. Every square is either inside the loop or outside it. A line between two squares means one is in and the other out; a cross means they are on the same side; the board's edge counts as outside. Shade squares mentally (or in your head as "in" and "out") and follow the chains: when two neighbouring squares turn out to be on the same side, the gap between them is crossed; on different sides, it's a line. A 3 has exactly three neighbours on the other side from itself, a 1 exactly one - that often tells you which side a square is on.

Strategy tips

• Start with 0s and 3s. They give the most at the start, especially in corners and along the edges.
• Cross freely. Crosses cost nothing and make the next step visible. A dot with two crosses and a line is a dot that must continue.
• Follow the loose ends. Every loose end of a line must keep going. Ask where each one can go next; often only one gap is left.
• Watch for small loops. Before you draw the line that closes a loop, check that no other lines are left outside it.
• Think in and out. When you're stuck on Crazy, decide which squares are inside the loop. The edge of the board is outside, so begin there and work inwards.
• For a fast time, draw long stretches with one drag instead of separate taps, and don't spend time crossing gaps you don't need.

Difficulty levels

The difficulty sets the size of the board and how far the reasoning goes. Every puzzle is checked by a solver that uses the techniques above in order, simplest first, and a puzzle belongs to a level only if it actually needs that level's technique.

• Easy: 5 by 5. Counting squares and dots, plus the corner patterns of single numbers.
• Normal: 7 by 7. Needs pairs of numbers read together, or the "don't close too early" rule.
• Hard: 8 by 8. Needs parity: counting the loop's crossings along a row or column.
• Crazy: 9 by 9. Needs inside-and-outside reasoning, the deepest technique here.

The board sizes stop at 9 by 9 so that every gap stays easy to tap on a small phone.

The results screen shows your time, your best time at that difficulty (marked when you set a new one), the mistakes you made when playing with 3 lives, the size of the board and the puzzle's code. Your statistics - wins, losses, win rate and streaks - are kept separately for each difficulty.