Slant

Reading the corner numbers

Every cell in Slant gets exactly one diagonal (a forward slash or a backslash), and the small numbers sit on the corners where cells meet. A number tells you precisely how many diagonal ends touch that corner. That's the whole clue system, and the easy wins come from the extremes: a 0 means no diagonal may point at that corner, and a 4 means all four surrounding cells must aim their line into it. Clicking a cell cycles it blank, then slash, then backslash, then blank again.

Openings you can play on sight

Start at the four corners of the board itself. The corner point of the grid touches only one cell, so a clue there settles that cell instantly. A 1 on the top-left point forces a backslash in that corner cell, because a backslash is the only diagonal with an end at that point. A 0 there forces the slash instead. Points along the outer edge touch just two cells, so a 2 on the edge fills both of them at once, and a 0 turns both away. On most grids these free moves alone carry you a good way in before you have to think hard.

The numbers keep working as the grid fills. Say a middle point shows 2 and two diagonals already run into it: the two unfilled cells around that point are now forced to lean away. The same goes for a 1 that already has its end. Every other cell at that corner must point elsewhere. This is why it pays to re-scan the neighbours each time you commit a cell. One placement often triggers two or three more, and good solvers ride those chains instead of hunting randomly around the board.

The rule that catches everyone

The numbers are only half the puzzle. The other rule is that your diagonals may never form a closed loop, and that's where careful solvers still trip. You can satisfy every corner number and still lose because a handful of slashes have quietly linked up into a ring.

Here's a way to track it. Think of the corner points as stations and every diagonal as a piece of track joining two of them. Each line you draw welds two groups of stations into one bigger group. If a new diagonal would join two stations that are already connected through some chain of track, it would close a ring, so that cell must take the other diagonal. You don't need to check the whole board on every move. Watch the long chains, because they're the only ones that can bite their own tail. Tight clusters of 1s are common loop traps, and late in a solve the loop rule is often what decides the last few stubborn cells when the numbers alone leave two choices open.

When you stall

Don't guess. Every Slant has a single solution you can reach by logic, so a stall just means there's a read you haven't made yet. Run three checks in order. First, look for any corner whose remaining cells are all forced by its count. Second, follow your longest chain and see whether some empty cell is the only thing that could join its two ends. Third, revisit part-filled corners near your newest lines, since every fresh diagonal changes the counts around it. One of the three almost always turns up a move, and it's far faster than backtracking out of a wrong guess. The board is done when every cell holds a line, every number is satisfied, and no loop has formed.

Gokigen Naname

Slant is known in Japan as Gokigen Naname, another puzzle in the Nikoli family, the Tokyo magazine house that made Sudoku famous. The name is a small joke: gokigen naname is a Japanese idiom for being in a bad mood, and it literally means your mood is on a slant. The puzzle reached a lot of western players through Simon Tatham's free puzzle collection, where it also goes by Slant. The appeal is how little it asks (one of two diagonals per cell) and how much logic it wrings out of that. The no-loop constraint is the clever twist that turns a plain counting exercise into a real deduction puzzle, and it's timed here, so smooth reading beats trial and error.