What is Slant?
Slant - known in Japan as Gokigen Naname - is a pencil puzzle where you draw a single diagonal line in every cell of a grid. Each diagonal runs corner to corner, so it is either a backslash that goes from the top-left to the bottom-right, or a forward slash that goes from the top-right to the bottom-left. There is no third option and no blank: every cell ends up with exactly one of the two slants.
What turns this into a puzzle are the small numbered circles sitting on the grid points - the corners where cells meet. Each number tells you exactly how many of the diagonals around that point reach it. A point can have up to four cells around it, so the clues run from 0 to 4. On top of that there is one global rule that gives Slant its bite: the diagonals you draw must never join up into a closed loop. Satisfy every number and avoid every loop, and the grid has just one possible pattern of slants.
- Every cell holds one diagonal: a backslash or a forward slash.
- Numbered circles sit on the points where cell corners meet.
- A number says how many diagonals touch that point, from 0 to 4.
- The diagonals must never form a closed loop anywhere on the grid.
- A correct grid satisfies every number and contains no loops.
- Each puzzle here is built to have exactly one solution.
How to play Slant online
Click or tap any cell to drop a diagonal in it. Each click cycles the cell forward - empty, then a backslash, then a forward slash, then empty again - so two clicks at most reach whichever slant you want, and a third clears it. If you prefer, right-click a cell to cycle the other way, which is a quick way to flip a single cell without scrolling through all three states. The numbered circles update live: a circle turns green the moment the diagonals around it match its number, and red if too many diagonals reach it.
The board also watches for loops. If the lines you have drawn ever close a circuit, the cells on that loop are highlighted and a short warning appears, so you can undo the move that sealed it. Check compares your grid with the unique solution and flags any cell that disagrees, without saying which way it should face. Hint fills one correct cell - or corrects a wrong one - Undo steps back, Reset clears the grid, and Solution draws the finished pattern when you would rather study it than solve it.
- Left-click cycles a cell: empty, backslash, forward slash, empty.
- Right-click cycles the other way for a fast single flip.
- Clue circles turn green when satisfied and red when overshot.
- Closing a loop highlights the offending cells and warns you.
- Check, Hint, Undo, Reset and Solution work as you would expect.
Read the 0s and 4s first
The strongest clues in Slant are the extremes. A 0 means no diagonal may touch that point, so every cell sitting around it must slant away from it. In the middle of the board a 0 instantly fixes all four of its cells, each pointing its corner in the opposite direction; on an edge it fixes two cells, and in the very corner of the grid it fixes the single cell there. A 4 is the mirror image and only ever appears deep inside the grid: all four surrounding cells must aim their corners straight at it, forming a little star. Sweep the board for 0s and 4s before anything else and you will often fill a dozen cells without a moment's thought.
The corner and edge points carry their own quiet certainties. A point in the very corner of the grid touches just one cell, so its only sensible clues are 0 or 1, and either one pins that cell down completely. A 1 on a grid corner forces the single diagonal to point at it; a 0 forces it away. These tiny forced cells look unglamorous, but each one becomes a fact that the next deduction can lean on, so clearing them early pays off across the whole solve.
- A 0 forces every surrounding cell to slant away from that point.
- A 4 - only ever interior - aims all four cells at that point.
- A grid-corner clue (0 or 1) fixes its single cell immediately.
- An edge point touches two cells; a 0 or a 2 fixes both at once.
- Resolve every extreme clue before attempting subtler counts.
No loops is the rule that does the work
It is easy to read Slant as nothing but counting, but the no-loop rule is where the real deductions live. Picture two diagonals that already meet at a point and curve around through a few cells until only one gap remains in the circuit. Whatever diagonal would close that circuit is now illegal, which means the cell must take the other slant - even if no nearby number demanded it. This is the move that separates Slant from a pure arithmetic puzzle: a line can be forced purely because the alternative would seal a loop.
The smallest loop is a tidy diamond formed by four cells around a single point, so the no-loop rule bites earliest in the tight corners where slashes start to curl back on themselves. A good habit is to think of the diagonals as a growing network of connected points: every diagonal you draw links two points together, and you must never link two points that some chain of diagonals has already connected. Solvers who have met Slitherlink will recognise the instinct, except here you are forbidding loops everywhere rather than building one - the discipline is the same, the goal reversed.
- A diagonal is illegal if it would close a loop of connected points.
- That alone can force a cell with no number nearby.
- The smallest possible loop is a four-cell diamond around one point.
- Track which points are already linked by a chain of diagonals.
- Never join two points that are already connected - that makes a loop.
Counting, balancing and the chains between clues
Once the extremes are gone, the middle numbers become a balancing act. Treat each clue as a budget for the diagonals around it: as soon as a point has collected its number of slants, every remaining cell around it must point away, and if a point still needs slants but has only just enough cells left to supply them, those cells are all forced toward it. A 3 on an interior point, for instance, is almost as strong as a 4 - three of its four cells must aim in, so the moment one of them is shown to point away, the other three are locked.
The art of a hard Slant board is letting these small certainties travel. A cell fixed by a 0 may decide a corner of a neighbouring 2, which in turn leaves a 1 with only one way to be satisfied, which closes off a loop two cells further on. Nothing here needs guessing: every step is a short, local deduction, but they hand off to each other like links in a chain. Slide between the numbers and the no-loop rule, letting each tighten the other, and even a dense 10x10 unravels one forced diagonal at a time.
- When a point reaches its number, the rest of its cells point away.
- When a point's spare cells just cover its need, all of them point in.
- A 3 inside the grid forces three of four cells toward the point.
- Forced cells chain: each fact unlocks the next clue or blocks a loop.
- Alternate between count logic and loop logic on every pass.
Where Slant comes from
Slant is one of the many original puzzles published by Nikoli, the Japanese company that gave Sudoku its name and popularised a whole family of logic puzzles built on simple drawing rules. Its Japanese name, Gokigen Naname, is a small joke: the phrase is an everyday idiom for being in a grumpy, out-of-sorts mood, but naname literally means slanting or diagonal, so the title reads as both 'out of sorts' and 'all at angles'. The puzzle reached English-speaking solvers under the plain, descriptive name Slant.
Part of why Slant travelled so well is its sheer minimalism. There is no arithmetic beyond counting to four, no shading, no symbols to learn - just two possible strokes and a rule against loops - and yet the deductions reach surprising depth. It also found a second home in software: Slant is one of the puzzles in Simon Tatham's widely played Portable Puzzle Collection, which introduced it to a generation of solvers who had never seen a Nikoli magazine. That blend of a pencil-and-paper heritage and an easy digital life is why a tiny grid of diagonals is still a satisfying way to spend ten minutes.
Slant vs Slitherlink, Masyu and other loop puzzles
Slant shares DNA with the loop puzzles that Nikoli is famous for, but it inverts their central idea. In Slitherlink you read numbered cells and connect dots into exactly one closed loop; in Masyu you thread a single loop past black and white pearls. Slant uses the same vocabulary of points, edges and clues, but it asks you to draw a forest rather than a loop - a network of diagonals that may branch and spread but must never close on itself. The numbers count line-ends at a point much as Slitherlink's numbers count edges around a cell, so the deduction styles feel like cousins.
Compared with shading puzzles like Nonograms or Nurikabe, Slant is far more geometric: you are never filling regions, only choosing the tilt of a line, and the global constraint is topological rather than about runs or connectivity of shaded blocks. That makes it a friendly bridge puzzle. If you enjoy the forced-move chains of Slitherlink you will feel at home, and if you have only ever shaded grids, Slant is an easy and rewarding way to start thinking about lines and loops instead of blocks.
- Slitherlink: clues count edges; you build exactly one closed loop.
- Masyu: thread a single loop obeying black and white pearls.
- Slant: clues count diagonal-ends; you build a branching, loop-free network.
- Slant's constraint is topological - avoid loops - not about shading.
- It bridges nicely between loop puzzles and edge-counting puzzles.
Grid sizes and difficulty levels
The 6x6 boards are the place to build your reflexes: a small field of diagonals where the 0s, 4s and corner clues carry you a long way and the loops you need to dodge are easy to spot. On 8x8 there are more clue points and longer gaps between the certainties, so the no-loop rule starts to earn its keep and you learn to track which points are already linked. The 10x10 boards are full puzzles - long chains of forced diagonals, loops that threaten from several cells away, and deductions that travel across the grid before a single line is sure.
Difficulty changes how many clues you are given. Easy boards keep plenty of numbers, so most cells are nailed down by counting alone and the solving stays brisk. Medium thins the clues, leaving more cells that only the no-loop rule can decide. Hard strips the board back to a lean set of numbers - close to the minimum that still pins down a single answer - so you lean hard on loop logic and long chains. Whatever you choose, every board is checked by a solver before you see it and only those with exactly one solution are kept, so each puzzle is always solvable by pure logic, never by guessing.
- 6x6 - learn the 0s, 4s and corner clues with loops easy to see.
- 8x8 - more points, longer gaps, and real work for the no-loop rule.
- 10x10 - long forced chains and loops that threaten from afar.
- Easy, medium and hard change how many clue numbers you get.
- Every puzzle is verified to have exactly one solution.