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 Getting Four-Six With Nine Digits (Posted on 2008-03-16)
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.

 Submitted by K Sengupta Rating: 2.0000 (2 votes) Solution: (Hide) The 4664th four-six number when arranged in descending order of magnitude is 245986541. EXPLANATION: Eigenray has provided a nice analytic solution in this location, deriving total number of four-six numbers as 9500 being part of the said process.

Comments: ( You must be logged in to post comments.)
 Subject Author Date re: less computer-dependent solution K Sengupta 2008-03-21 10:59:21 Solution, agreed ed bottemiller 2008-03-17 20:44:37 Nine Loops ed bottemiller 2008-03-17 20:33:17 correction to last post xdog 2008-03-17 10:41:06 No Subject xdog 2008-03-17 09:59:32 less computer-dependent solution Eigenray 2008-03-17 02:52:41 re(2): computer solution Charlie 2008-03-16 20:33:46 re: computer solution Ady TZIDON 2008-03-16 20:08:49 computer solution Charlie 2008-03-16 16:03:15

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