The Doppit Almanac · No. 47
Leanit
Slant every cell to match its corner numbers
What it is
Leanit is a slant puzzle, known elsewhere as Gokigen Naname. Every cell takes one slant, leaning up or down, and no cell is left empty. The numbers sit on the corners between cells and count the slant ends that meet there. Fill the grid so every number ends up with the count printed on it, and so the slants never close a loop.
A corner is shared by up to four cells, and each of them either points an end at it or leans away. A 4 takes an end from all four cells and a 0 takes none, so both settle their whole corner on sight. The numbers in between are the ones you count: three ends already at a 3, and every cell left around it leans away. Then there is the loop rule, which decides cells the counting leaves open. Slants join end to end at the corners, and a run of them that comes back on itself is not allowed, so a slant that would close a loop leans the other way.
How it plays
- Every cell holds exactly one slant, leaning up or down.
- A number takes exactly that many slant ends at its corner. A 0 takes none.
- A corner with no number takes any number of ends.
- The slants never close a loop. No run of them ever comes back on itself.
- Pick Up or Down, then tap or drag to place slants. Tap a slant again to lift it.
- A number that can no longer be met turns red, and so does a loop. Hint shows the next forced slant and says why.
The difficulties
Easy is four by four, sixteen slants, and never asks you to suppose anything. Counting the corners settles it, with the loop rule deciding a cell on most boards. Medium is six by six and asks at most twice: lean a cell one way, follow what that forces, and find a number given more ends than it takes, or left too few cells to reach its count, or a loop closed. Then the cell leans the other way. Hard is seven by seven and wants that move once at least, six times at most. Expert is eight by eight and asks nothing new, only more of the same: seven suppositions at the least, fourteen at the most, which is why it runs long. A fresh board is dealt every day, for nothing.
Play today's board