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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)

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Solution computer solution | Comment 1 of 9

FOR a = 1 TO 6
FOR b = a + 1 TO 7
FOR c = b + 1 TO 8
FOR d = c + 1 TO 9
FOR e = 4 TO d - 1
FOR f = 3 TO e - 1
FOR g = 2 TO f - 1
FOR h = 1 TO g - 1
FOR i = 0 TO h - 1
 ct = ct + 1
 IF ct < 20 OR ct > 4645 THEN
 PRINT ct, a; b; c; d; e; f; g; h; i
 END IF
 IF ct = 4664 THEN GOTO version2
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT

finds (to show the first 19, and the last few up to and including the 4664th):

1             1  2  3  5  4  3  2  1  0
2             1  2  3  6  4  3  2  1  0
3             1  2  3  6  5  3  2  1  0
4             1  2  3  6  5  4  2  1  0
5             1  2  3  6  5  4  3  1  0
6             1  2  3  6  5  4  3  2  0
7             1  2  3  6  5  4  3  2  1
8             1  2  3  7  4  3  2  1  0
9             1  2  3  7  5  3  2  1  0
10            1  2  3  7  5  4  2  1  0
11            1  2  3  7  5  4  3  1  0
12            1  2  3  7  5  4  3  2  0
13            1  2  3  7  5  4  3  2  1
14            1  2  3  7  6  3  2  1  0
15            1  2  3  7  6  4  2  1  0
16            1  2  3  7  6  4  3  1  0
17            1  2  3  7  6  4  3  2  0
18            1  2  3  7  6  4  3  2  1
19            1  2  3  7  6  5  2  1  0

...


4646          2  3  8  9  8  7  5  3  2
4647          2  3  8  9  8  7  5  4  0
4648          2  3  8  9  8  7  5  4  1
4649          2  3  8  9  8  7  5  4  2
4650          2  3  8  9  8  7  5  4  3
4651          2  3  8  9  8  7  6  1  0
4652          2  3  8  9  8  7  6  2  0
4653          2  3  8  9  8  7  6  2  1
4654          2  3  8  9  8  7  6  3  0
4655          2  3  8  9  8  7  6  3  1
4656          2  3  8  9  8  7  6  3  2
4657          2  3  8  9  8  7  6  4  0
4658          2  3  8  9  8  7  6  4  1
4659          2  3  8  9  8  7  6  4  2
4660          2  3  8  9  8  7  6  4  3
4661          2  3  8  9  8  7  6  5  0
4662          2  3  8  9  8  7  6  5  1
4663          2  3  8  9  8  7  6  5  2
4664          2  3  8  9  8  7  6  5  3

so the answer is 238987653.


  Posted by Charlie on 2008-03-16 16:03:15
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