7

Part of 1998 Switzerland Team Selection Test

Problems(1)

entry at intersection of i-th row and the j-th column equals i+ j -1

Source: Switzerland - Swiss TST 1998 p7

n\times n

matrix whose entry at the intersection of the

i

-th row and the

j-

th column equals

i+ j -1

. What is the largest possible value of the product of

n

entries of the matrix, no two of which are in the same row or column?