Combinatorics · Parity · Tetrominoes · Tilings · Colourings · Constructions
A natural number is written in every cell of a square table. Call the table interesting if the sum of all the numbers in it is odd and, in addition, the sum of the four numbers covered by any placement of the piece below is odd. The piece may be rotated and reflected, but it must lie entirely inside the table.
Decide, with proof, whether an interesting table exists of dimensions
(a) \(3 \times 3\); (b) \(5 \times 5\); (c) \(4 \times 4\).
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2009, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source