Five Cells — the puzzle that divides

Five Cells is a Nikoli puzzle that involves dividing the grid into regions of five cells (pentominoes).

Rules

• Divide the grid into blocks of five cells each (connected orthogonally).
• The numbers in the cells indicate how many sides of that cell are part of a block’s border (including the outer edge of the grid).

Example

Here’s a 5×5 Five Cells puzzle to start with:

Basic Strategy

A cell with a 0 is always at the center of a cross-shaped block (it has no walls around it, so all four of its neighbors belong to the same block).

Two adjacent cells with a 3 can never belong to the same block (each has three sides on a border, making it impossible to connect them within a valid pentomino).

The puzzle is NP-complete, meaning there is no simple algorithm to solve it — every grid is a unique challenge!

Solution

If you get stuck, here’s the solution: