MathDB

3. We have a

n \times n

board. We color the unit square

(i,j)

black if

i=j

, red if

i<j

and green if

i>j

. Let

a_{i,j}

be the color of the unit square

(i,j)

. In each move we switch two rows and write down the

n

-tuple

(a_{1,1},a_{2,2},\cdots,a_{n,n})

. How many

n

-tuples can we obtain by repeating this process? (note that the order of the numbers are important)

P3