MathDB

There is an

n*n

table with some unit cells colored black and the others are white. In each step , Amin takes a

row

with exactly one black cell in it , and color all cells in that black cell's

column

red. While Ali , takes a

column

with exactly one black cell in it , and color all cells in that black cell's

row

red. Prove that Amin can color all the cells red , iff Ali can do so.

4