What is Slant?
Slant fills a grid with diagonal lines, one per square, each running either \ or /. Numbers sit on the corners where grid lines cross, and each says how many diagonals touch that corner. The catch is that the lines must never close a loop.
In Japan it’s called Gokigen Naname, a play on a phrase for being in a bad mood (naname means slanted). It comes from Nikoli, the publisher behind many of the classic Japanese logic puzzles.
How to start a Slant
Begin at the edges. A corner of the grid touches only one square, so a 1 there means that square’s line points into the corner and a 0 means it points away. Numbers on the border touch two squares, so a 2 on the edge fixes both of them, and a 0 does too.
Inside the grid, a 4 fixes all four squares around it and a 0 does the same the other way. After that, look for numbers that have already reached their count: every other square around them points away.
Then watch for loops. Whenever three sides of a small diamond are drawn, the fourth line must go the other way, or it would close the loop.
Common mistakes
It’s easy to count the lines touching a corner wrong. Only lines that end exactly on that corner count, not lines passing near it.
Loops can be bigger than one diamond. If two lines would meet up with a long chain you drew earlier, that also closes a loop.
Questions
- What counts as a loop?
- Any closed shape made of diagonal lines, of any size, from a single small diamond to a long winding ring. The finished grid has none at all.
- Does every square need a line?
- Yes. Each square gets exactly one diagonal, \ or /. Corners without a number can have any number of lines touching them.
- Does every Slant have one solution?
- Every Slant on this site has exactly one, checked by a solver, so it can be finished by logic without guessing.
- How big are the puzzles?
- The daily Slant is 7×7. Practice puzzles come in 5×5, 7×7 and 10×10.