MathDB

Define the distance between two

5

-digit numbers

\overline{a_1a_2a_3a_4a_5}

and

\overline{b_1b_2b_3b_4b_5}

to be the largest integer

j

such that

a_j \ne b_j

. (Example: the distance between

16523

and

16452

5

.) Suppose all

5

-digit numbers are written in a line in some order. What is the minimal possible sum of the distances of adjacent numbers in that written order?

Problem Statement