MathDB

Let

T

be a

2015 \times 2015

array containing the integers

1, 2, 3, ... , 2015^2

satisfying the property that

T_{i,a }> T_{i,b}

for all

a > b

and

T_{c,j} > T_{d,j}

for all

c > d

where

1 \le a, b, c, d \le 2015

and

T_{i,j}

represents the entry in the

i

-th row and

j

-th column of

T

. How many possible values are there for the entry at

T_{5,5}

9