Slant
Fill every cell with a diagonal line
Slant (also called Gokigen Naname) is a diagonal-placement puzzle where every cell gets either a forward slash (/) or backslash (\). Numbers at grid intersections (where four cells meet) tell you how many of those cells' diagonals touch that intersection point. Additionally, the diagonals must not form any closed loops. The combination of local number constraints with the global no-loop rule creates an elegant deduction puzzle with a distinctive visual style.
How to Play Slant
One Diagonal Per Cell
Every cell must contain either a forward slash (/) or a backslash (\). No cell is left empty.
Intersection Numbers
Numbers at grid intersections tell you exactly how many of the surrounding diagonals touch that point.
No Loops
The diagonals must not form any closed loops. Every path of connected diagonals must eventually reach the grid border.
Corner Intersections
Intersection points on the grid border have fewer surrounding cells (2 on edges, 1 in corners), making their clues more constraining.
Unmarked Intersections
Intersections without numbers can have any count of touching diagonals. Only numbered intersections constrain you.
Complete Coverage
Fill every cell. The puzzle is solved when all number clues are satisfied and no loops exist.
Strategy & Solving Tips
Expert Slant solving uses intersection clues to determine local diagonal orientations, then applies the no-loop rule for global consistency.
- A "0" at any intersection means none of the surrounding diagonals touch it — this immediately determines those cells' orientations
- A "4" at an interior intersection means all four surrounding diagonals point toward it — also immediately determined
- Corner intersections with "0" or "1" are extremely constraining since they have only one surrounding cell
- After placing diagonals, check for potential loops by tracing connected paths — if a path could close, break it
- Edge intersections have at most 2 surrounding cells, so "0" or "2" at edges determines both cells immediately
- Use the loop rule as a tiebreaker: if both diagonal orientations satisfy number clues but one creates a loop, choose the other
Slant FAQ
What counts as a "loop"?
A loop is a closed path formed by connected diagonal lines that never reaches the grid edge. Imagine tracing along the diagonals — if you return to where you started without hitting a border, that's a forbidden loop.
Do all intersections have numbers?
No. Only some intersections have numbers. Unmarked intersections impose no constraint on how many diagonals touch them. The numbered intersections provide enough information to solve the puzzle.
What does a number at a corner of the grid mean?
A corner intersection borders only one cell. So "0" means the diagonal in that cell points away from the corner, and "1" means it points toward it.
Is Slant related to other puzzles?
Slant is a member of the Nikoli puzzle family. Its diagonal mechanic is unique, but the combination of local constraints (numbers) with a global constraint (no loops) is a design principle shared by many elegant logic puzzles.
Ready to Play Slant?
Draw your way to the solution in Slant — the diagonal puzzle where numbers guide each cell and the no-loop rule ties everything together. Simple pieces, elegant logic.