Question 24
Each of the small squares of a $50 \times 50$ table is coloured in red or blue. Initially all squares are red. A step means changing the colour of all squares on a row or on a column.
a) Prove that there exists no sequence of steps, such that at the end there are exactly $2011$ blue squares.
b) Describe a sequence of steps, such that at the end exactly $2010$ squares are blue.
a) Prove that there exists no sequence of steps, such that at the end there are exactly $2011$ blue squares.
b) Describe a sequence of steps, such that at the end exactly $2010$ squares are blue.