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 computer solution by Charlie)

The  4-6 numbers are not arranged  in a  descending order.

The resulting answer is probably wrong.

 

Ady

 

Edited on March 16, 2008, 8:13 pm

Posted by Ady TZIDON on 2008-03-16 20:08:49