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November 17th, 2011, 08:11 AM   #1
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Computing values

Given a number N between 2 and 9, consider the integers that can be formed using
each digit in the set {1, 2, . . . ,N} exactly once. For instance, if N is 3, the integers we
can form are 123, 231, 312, 132, 321 and 213. If we arrange these in increasing order,
we get the list {123, 132, 213, 231, 312, 321}. The fourth number in this list is 231.
In general, given two numbers N and K, the task is to compute the number at position
K when all integers formed using the digits {1, 2, . . . ,N} exactly once are arranged in
ascending order. For instance, the example worked out above corresponds to N = 3
and K = 4.
Compute the answer for the following values of N and K.
(a) N = 5, K = 76 (b) N = 7, K = 4197 (c) N = 9, K = 191082
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