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Problem 38

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Pandigital Multiples

Take the number $192$ and multiply it by each of $1$, $2$, and $3$:

$192\times 1=192$

$192\times 2=384$

$192\times 3=576$

By concatenating each product we get the $1$ to $9$ pandigital, $192384576$. We will call $192384576$ the concatenated product of $192$ and $(1,2,3)$

The same can be achieved by starting with $9$ and multiplying by $1$, $2$, $3$, $4$, and $5$, giving the pandigital, $918273645$, which is the concatenated product of $9$ and $(1,2,3,4,5)$.

What is the largest $1$ to $9$ pandigital 9-digit number that can be formed as the concatenated product of an integer with $(1,2,\dots ,n)$ where $n>1$?

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全数字的倍数

将$192$分别与$1$、$2$、$3$相乘：

$192\times 1=192$

$192\times 2=384$

$192\times 3=576$

将这些乘积拼接起来，可以得到一个$1$至$9$全数字的数$192384576$，因此称$192384576$为$192$和$(1,2,3)$的拼接乘积。

类似地，将$9$分别与$1$、$2$、$3$、$4$、$5$相乘，可以得到$1$至$9$全数字的数$918273645$，并称之为$9$和$(1,2,3,4,5)$的拼接乘积。

考虑所有$n>1$时某个整数和$(1,2,\dots ,n)$的拼接乘积，其中最大的$1$至$9$全数字的数是多少？

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