- ... is contiguous (all cells connect via edges, not just vertices).
- ... has exactly one of the ten numbers shown in the grid.
- ... contains as many cells as the number that it contains.
- ... borders (along edges, not vertices) the same number of other areas as the number that it contains; for example, a 6-cell area will border six other areas, again based on the digit 6 that is contained within its bounds.
An example of a completed puzzle of this type is
Puzzle by Thinh Van Duc Lai, from N.Y.Times Magazine, March 17, 2019.