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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.

  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 solutionK Sengupta2008-03-21 10:59:21
Solution, agreeded bottemiller2008-03-17 20:44:37
Nine Loopsed bottemiller2008-03-17 20:33:17
correction to last postxdog2008-03-17 10:41:06
No Subjectxdog2008-03-17 09:59:32
Solutionless computer-dependent solutionEigenray2008-03-17 02:52:41
Solutionre(2): computer solutionCharlie2008-03-16 20:33:46
re: computer solutionAdy TZIDON2008-03-16 20:08:49
Solutioncomputer solutionCharlie2008-03-16 16:03:15
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