MathDB

Let

X

be a

5\times 5

matrix with each entry be

0

1

. Let

x_{i,j}

be the

(i,j)

-th entry of

X

(i,j=1,2,\hdots,5). Consider all the

24

ordered sequence in the rows, columns and diagonals of

X

in the following: \begin{align*} &(x_{i,1}, x_{i,2},\hdots,x_{i,5}),\ (x_{i,5},x_{i,4},\hdots,x_{i,1}),\ (i=1,2,\hdots,5) \\ &(x_{1,j}, x_{2,j},\hdots,x_{5,j}),\ (x_{5,j},x_{4,j},\hdots,x_{1,j}),\ (j=1,2,\hdots,5) \\ &(x_{1,1},x_{2,2},\hdots,x_{5,5}),\ (x_{5,5},x_{4,4},\hdots,x_{1,1}) \\ &(x_{1,5},x_{2,4},\hdots,x_{5,1}),\ (x_{5,1},x_{4,2},\hdots,x_{1,5}) \end{align*} Suppose that all of the sequences are different. Find all the possible values of the sum of all entries in

X

Problem Statement