  We prove that octants are cover-decomposable into multiple coverings, i.e.,
for any k there is an m(k) such that any m(k)-fold covering of any subset of
the space with a finite number of translates of a given octant can be
decomposed into k coverings. As a corollary, we obtain that any m(k)-fold
covering of any subset of the plane with a finite number of homothetic copies
of a given triangle can be decomposed into k coverings. Previously only some
weaker bounds were known for related problems.
