Arranging apples in an array

Departing from a real-world problem we consider a greedy algorithm which either finds a 0–1 matrix with prescribed row and column sums or terminates with the conclusion that no such matrix exists.The problem has been pending in the literature for about 30 years. Our proof of the validity of the algorithm is established along with an account of earlier findings and appears to be considerably simpler than any other proof hitherto proposed. Various open questions conclude the paper.Dedicated to Peter Naur on the occasion of his 60th birthday