In [Am. Math. Mon. 94, 601-617 (1987; Zbl 0691.05011)], S. Wagon gives 14 proofs of the fact that if a rectangle \(R\) is tiled with rectangles, each having at least one side of integral length, then \(R\) has a side of integral length. In the present paper the author provides an algorithm for deciding when a rectilinear polygon (that is, a polygon with sides parallel to the axes) can be tiled with rectangles, each having an integer side.