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.

Due to a mis-reading of the problem I posted the wrong answer.

fwiw, I concur that the 4664th 4-6 9-digit integer is 245986541.

 

Posted by xdog on 2008-03-17 10:41:06