Problem

Source: Ukraine 2005 grade 9

Tags: combinatorics unsolved, combinatorics



Under the rules of the "Sea battle" game (no two ships may have a common point), can the following sets of rectangular ships be arranged on a 10×10 square board: (a) two ships 1×4, 4 ships 1×3, 6 ships 1×2, and 8 ships 1×1; (b) two ships 1×4, 4 ships 1×3, 6 ships 1×2, 6 ships 1×1, and 1 ship 2×2; (c) two ships 1×4, 4 ships 1×3, 6 ships 1×2, 4 ships 1×1, and 2 ships 2×2?