Nine digit positive integers of the form PQRSTUVWX are called four-six numbers if the digits P, Q, R and S (in this order) are in strictly ascending order of magnitude, while the digits S, T, U, V, W and X (in this order) are in strictly descending order of magnitude.

For example, each of 567876543 and 678986430 is a four-six number, but 567876654 is NOT a valid four-six number since the digits 876654 (in this order) are not in strictly descending order of magnitude. Similarly, 678875432 is NOT a valid four-six number since the digits 6788 (in this order) are not in strictly ascending order of magnitude.

All the possible four-six numbers are now arranged in descending order of magnitude.

What is the 4664^{th} number?

__Note__: No four-six number can contain leading zeroes.

(In reply to

less computer-dependent solution by Eigenray)

Very nice *analytic methodology* deriving the total count of four six numbers as part of the process.

Consequently, I confirm having hyperlinked your methodology in my solution.

*Edited on ***March 21, 2008, 3:45 pm**