Cell Blocks

Two puzzles from the same family. Rectangles is Shikaku, published by Nikoli as Divide by Box: split the grid so every block is a rectangle holding one number equal to its area. Polyominoes is Fillomino, where blocks take any shape and two regions of the same size may never touch — which is what kills the tidy divisor arithmetic the first mode relies on.

Every puzzle is generated in your browser, checked to have exactly one solution, and stamped with the deepest rule its solution actually needs. The stamp is honest: hard mode sometimes lands a strong Grade III rather than a Grade IV, and says so.

The maths behind it, at length: The mathematics of Cell Blocks.