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.
(In reply to
re: computer solution by Ady TZIDON)
You're right.
The corrected program:
FOR a = 6 TO 1 STEP -1
FOR b = 7 TO a + 1 STEP -1
FOR c = 8 TO b + 1 STEP -1
FOR d = 9 TO c + 1 STEP -1
FOR e = d - 1 TO 4 STEP -1
FOR f = e - 1 TO 3 STEP -1
FOR g = f - 1 TO 2 STEP -1
FOR h = g - 1 TO 1 STEP -1
FOR i = h - 1 TO 0 STEP -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 END
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT
resulting in:
1 6 7 8 9 8 7 6 5 4
2 6 7 8 9 8 7 6 5 3
3 6 7 8 9 8 7 6 5 2
4 6 7 8 9 8 7 6 5 1
5 6 7 8 9 8 7 6 5 0
6 6 7 8 9 8 7 6 4 3
7 6 7 8 9 8 7 6 4 2
8 6 7 8 9 8 7 6 4 1
9 6 7 8 9 8 7 6 4 0
10 6 7 8 9 8 7 6 3 2
11 6 7 8 9 8 7 6 3 1
12 6 7 8 9 8 7 6 3 0
13 6 7 8 9 8 7 6 2 1
14 6 7 8 9 8 7 6 2 0
15 6 7 8 9 8 7 6 1 0
16 6 7 8 9 8 7 5 4 3
17 6 7 8 9 8 7 5 4 2
18 6 7 8 9 8 7 5 4 1
19 6 7 8 9 8 7 5 4 0
...
4646 2 4 5 9 8 7 5 3 2
4647 2 4 5 9 8 7 5 3 1
4648 2 4 5 9 8 7 5 3 0
4649 2 4 5 9 8 7 5 2 1
4650 2 4 5 9 8 7 5 2 0
4651 2 4 5 9 8 7 5 1 0
4652 2 4 5 9 8 7 4 3 2
4653 2 4 5 9 8 7 4 3 1
4654 2 4 5 9 8 7 4 3 0
4655 2 4 5 9 8 7 4 2 1
4656 2 4 5 9 8 7 4 2 0
4657 2 4 5 9 8 7 4 1 0
4658 2 4 5 9 8 7 3 2 1
4659 2 4 5 9 8 7 3 2 0
4660 2 4 5 9 8 7 3 1 0
4661 2 4 5 9 8 7 2 1 0
4662 2 4 5 9 8 6 5 4 3
4663 2 4 5 9 8 6 5 4 2
4664 2 4 5 9 8 6 5 4 1
so the answer actually is 245986541.
Edited on March 16, 2008, 8:34 pm
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Posted by Charlie
on 2008-03-16 20:33:46 |
re(2): computer solution
