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Problem 24

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Lexicographic permutations

A permutation is an ordered arrangement of objects. For example, $3124$ is one possible permutation of the digits $1$, $2$, $3$ and $4$. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of $0$, $1$ and $2$ are:

$$012 \quad 021 \quad 102 \quad 120 \quad 201 \quad 210$$

What is the millionth lexicographic permutation of the digits $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$ and $9$?

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字典序排列

排列指的是将一组对象放置为特定的顺序。例如，$3124$是数字$1$、$2$、$3$、$4$的一个排列。将所有排列按照数字大小或字母先后进行排序称为字典序。数字$0$、$1$、$2$的字典序排列是：

$$012 \quad 021 \quad 102 \quad 120 \quad 201 \quad 210$$

在数字$0$、$1$、$2$、$3$、$4$、$5$、$6$、$7$、$8$、$9$的字典序排列中，处于第一百万位的排列是什么？

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