The rules of Fields
A field is a group of same-colored cells joined by their edges. Your finished grid has to follow three rules:
- Every cell is green or blue.
- Every field holds exactly one number, and that number is the field's size in cells.
- Two fields of the same color cannot share an edge. They can touch at a corner.
Each numbered cell starts with its color already set, so a green 4 means a green field of exactly four cells. Every puzzle has one answer.
How to solve Fields
Black outlines below show the cells each step decides. All five techniques work on every board, from the easiest to the hardest.
1. Fence in a finished field
Once a field reaches its number, it can't grow. Every open cell along its edges takes the other color. Corners stay open, because a diagonal cell doesn't join the field.
2. Keep two numbers apart
A field can only hold one number. If an open cell touches two numbers of the same color, it must be the other color, or those two numbers would end up in one field.
3. Follow the only way out
A field that is still short of its number has to grow. When the other cells around it are taken, its one remaining path is forced. When the field reaches its number, fence it in.
4. Give stray cells a route to a number
A colored cell with no number still needs one, since every field holds exactly one. Inkwell calls these orphans. If an orphan has only one open neighbor, that neighbor must match it.
5. Count how far a number can reach
A number can only reach as far as its size allows. A cell that no green number can reach must be blue, and a cell that no blue number can reach must be green. Here the green 2 is the only green number nearby, so the far cells can't be green.
Fields and Light and Shadow
Outside Inkwell, you'll find these rules under the name Light and Shadow. Those boards usually use gray and white cells, but the goal is the same: split the grid into two-colored regions, each with one number that equals its size, and keep same-colored regions from sharing an edge. If you can solve one, you can solve the other, and the techniques above work on both.