Loop Puzzles
These four are about lines rather than squares. You are drawing a route — a closed loop, or a set of paths — and the clues tell you where it can and cannot go.
A Loop Has No Ends, And That Is The Strongest Clue
In slitherlink and masyu the answer is a single closed loop, which means every corner it reaches has either no lines or exactly two — a loop arrives and it leaves. That rule is worth more than the numbers, and it is the one beginners underuse.
It also rules things out. A line that would close a small loop early is illegal unless that loop already contains everything, which lets you discard candidates long before the grid is full.
Ruling A Line Out Is Half The Work
Every one of these puzzles has three states for a connection, not two: drawn, ruled out, and undecided. Marking a connection as impossible is what lets the next deduction happen — a corner only forces a line once its other sides are gone.
Numberlink And Hashi Are Counting Problems In Disguise
Numberlink looks like route-finding and is really about degree: a numbered square is the end of a path so exactly one line touches it, and every other square is passed through so exactly two do. Hashi is the same idea with a number written on it. Once you see them that way, both stop being about drawing and start being about arithmetic on connections.
| Type | What you draw | The rule that does the most work |
|---|---|---|
| Slitherlink | One closed loop on the dot grid | Every dot has no lines or exactly two |
| Masyu | One closed loop through the cells | An edge that would close a short loop is impossible |
| Numberlink | A path between each pair | Every square is used, so untouched squares are forced |
| Hashi | Bridges between islands | An island needing 8 must take two bridges in all four directions |
Printing A Loop Puzzle
Loop puzzles print unusually well because the answer is a line, and a line is easier to draw than to click. Printing drops the interface and keeps the grid, the clues and the explanation. On paper you lose the undo, so mark impossible edges with a small cross exactly as you would on screen — it is the same technique either way.
The One Habit That Separates Fast Solvers
Beginners look at the numbers. Experienced solvers look at the corners. In slitherlink and masyu every corner has either no lines or exactly two, and that rule fires constantly while the clues sit there saying nothing new. Scan the corners after every deduction and the grid opens up in a way that re-reading the numbers never achieves.
The same instinct works in numberlink and hashi, where the equivalent is counting how many connections a square or island still has available.
| You see | In | What it settles immediately |
|---|---|---|
| A 0 | Slitherlink | All four of that cell’s sides are out |
| A 3 next to a 0 | Slitherlink | Three sides forced, and the direction of the loop |
| Two black circles adjacent | Masyu | The edge between them can never be drawn |
| A white circle at the edge | Masyu | The line runs along the edge, since it must go straight |
| An island needing 8 | Hashi | Two bridges in all four directions |
| A number in a corner | Numberlink | Only two ways its path can start |
Loop Puzzles Frequently Asked Questions
What is a loop puzzle?
A puzzle where the answer is a line rather than a set of filled squares. In slitherlink and masyu it is one closed loop; in numberlink it is a set of paths joining pairs; in hashi it is bridges joining islands. The clues restrict where the line may run.
Which loop puzzle is the friendliest start?
Masyu, because it has exactly two rules and both are visual: a white circle needs the line to pass straight through, a black circle needs it to turn. Slitherlink is next. Numberlink and hashi feel different because they are about joining specific points rather than making one loop.
Why does a zero in slitherlink matter so much?
Because it settles four connections at once — a cell marked 0 uses none of its sides, so all four are ruled out immediately. Zeros are the best opening move on any slitherlink grid, and a grid with several of them is much gentler than its size suggests.
Can paths cross in numberlink?
No. Paths never cross and never share a square, and in the puzzles here no path ever touches itself either — two squares of the same path are never neighbours unless they are consecutive along it. That last condition is what keeps each puzzle to a single answer.
Do these ever need guessing?
No. Each puzzle is checked before it is shown: a solver using only human techniques must finish it unaided, and a separate search must confirm there is exactly one answer. Anything failing either check is discarded.
Related Practice
Shading puzzles apply the same rule-out habit to squares instead of lines. Number logic puzzles swap the route for digits, and paper folding is the spatial cousin of both.