In a 10 by 10 square grid (which we call “the bay”) you are requested to place ten “ships”: one 1 by 4 ship, two 1 by 3 ships, three 1 by 2 ships and four 1 by 1 ships. The ships may not have common points (even corners) but may touch the “shore” of the bay. Prove that(a) by placing the ships one after the other arbitrarily but in the order indicated above, it is always possible to complete the process;
(b) by placing the ships in reverse order (beginning with the smaller ones), it is possible to reach a situation where the next ship cannot be placed (give an example). (KN Ignatjev) combinatoricscombinatorial geometryTiling