Proof of Quilt

The puzzle Proof of Quilt is one of many pencil-and-paper puzzles.
An instance of Proof of Quilt consists of an m × n rectangular board of unit squares. Each square is either white or black, and some black squares contain a number. A candidate solution to the puzzle consists of filling
in some of the white squares with a black half-square (isosceles right triangle filling half the area); white squares may also be left entirely white. Each number in a black square specifies the number of b/w squares that should be among four (vertically or horizontally adjacent) neighbors of the black square. (A black square without a number allows any number of b/w neighbors.) The objective of the puzzle is to fill the white squares in the given board while satisfying the above constraints and so that the remaining white area consists only of (empty) squares and rectangles.

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