There are cards numbered 1 to 9 lying on a table. It is known that they can be arranged in \(9!\) ways in a line. In how many ways can these cards be arranged (in a line) so that there are no 4 cards that are in ascending or descending order?
Example: In the sequence of numbers 3-2-1-6-5-4-9-8-7, there are no 4 cards in either ascending or descending order (from left to right).
Details and assumptions:
- The 4 cards need not be adjacent to each other.
- The numbers are read from left to right in the line.
- Source: numberphile