Question 144
Suppose you have two types of tetrominoes:
the two on the left are called "S-type", and the two on the right are called "Z-type". Consider a white chessboard of infinite size, on which we pick several squares and paint them black. Assume that we can use only S-type tetrominoes to cover all black squares without covering any white one. Prove that, if we use S- and/or Z-type tetrominoes to cover all black squares instead, without covering any white one, then we must use an even number of Z-type tetrominoes.
(The tetrominoes again, for reference:)
the two on the left are called "S-type", and the two on the right are called "Z-type". Consider a white chessboard of infinite size, on which we pick several squares and paint them black. Assume that we can use only S-type tetrominoes to cover all black squares without covering any white one. Prove that, if we use S- and/or Z-type tetrominoes to cover all black squares instead, without covering any white one, then we must use an even number of Z-type tetrominoes.
(The tetrominoes again, for reference:
)