  Shimizu introduced a region crossing change unknotting operation for knot
diagrams. As extensions, two integral region choice problems were proposed and
the existences of solutions of the problems were shown for all non-trivial knot
diagrams by Ahara and Suzuki, and Harada. We relate both integral region choice
problems with an Alexander numbering for regions of a link diagram, and give
alternative proofs of the existences of solutions for knot diagrams. We also
discuss the problems on link diagrams. For each of the problems on the diagram
of a two-component link, we give a necessary and sufficient condition that
there exists a solution.
