MathDB

To each number with

n^2

digits, we associate the

n\times n

determinant of the matrix obtained by writing the digits of the number in order along the rows. For example :

8617\mapsto \det \left(\begin{matrix}{\;8}& 6\;\\ \;1 &{ 7\;}\end{matrix}\right)=50

. Find, as a function of

n

, the sum of all the determinants associated with

n^2

-digit integers. (Leading digits are assumed to be nonzero; for example, for

n = 2

, there are

9000

determinants.)

Problem Statement