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Getting Four-Six With Nine Digits (Posted on 2008-03-16) Difficulty: 3 of 5
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 4664th number?

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

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: less computer-dependent solution Comment 9 of 9 |
(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
  Posted by K Sengupta on 2008-03-21 10:59:21

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