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The Descending Integers (Posted on 2006-02-02) Difficulty: 3 of 5
Let us consider all possible positive whole numbers (not containing any leading zeroes) with the proviso that in each of the numbers, none of its digits can be repeated.

Note: any given number may or may not contain all the digits from 0 to 9 (Examples: 7; 20; 1056; 3067941825 etc.)

These numbers are now arranged in descending order of magnitude.

What would be the 200,136th number?

See The Solution Submitted by K Sengupta    
Rating: 2.8000 (5 votes)

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Solution re: solution -- computer confirmation | Comment 3 of 8 |
(In reply to solution by Charlie)

By taking the permutations of all ten digits in ascending order of value, and counting down from 10! = 3628800, when we get to a count of 200136, that will be the 200,136th in descending order.

DECLARE SUB permute (a$)
DEFLNG A-Z
CLS
a$ = "0123456789": h$ = a$
ct = 3628800
DO
  permute a$
  ct = ct - 1
LOOP UNTIL a$ = h$ OR ct = 200136
PRINT a$

The permute subroutine is shown elsewhere on this site.

The answer agrees, as 9403152678.


  Posted by Charlie on 2006-02-02 12:45:28
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