MathDB

To unlock his cell phone, Joao slides his finger horizontally or vertically across a numerical box, similar to the one represented in the figure, describing a

7

-digit code, without ever passing through the same digit twice. For example, to indicate the code

1452369

, Joao follows the path indicated in the figure. https://cdn.artofproblemsolving.com/attachments/8/a/511018ba4e43c2c6f0be350d57161eb5ea7c2b.png João forgot his code, but he remembers that it is divisible by

9

. How many codes are there under these conditions?

Problem Statement