Problem 571
Super Pandigital Numbers
A positive number is pandigital in base $b$ if it contains all digits from 0 to $b$ - 1 at least once when written in base $b$.
A n-super-pandigital number is a number that is simultaneously pandigital in all bases from 2 to $n$ inclusively.
For example 978 = 11110100102 = 11000203 = 331024 = 124035 is the smallest 5-super-pandigital number.
Similarly, 1093265784 is the smallest 10-super-pandigital number.
The sum of the 10 smallest 10-super-pandigital numbers is 20319792309.
What is the sum of the 10 smallest 12-super-pandigital numbers?
超级全数字数
如果一个正整数的$b$进制表示中出现数字0到$b$-1每个至少一次，则称其为$b$进制的全数字数。
如果一个正整数同时是从$2$到$n$进制的全数字数，则称其为n-超级全数字数。
例如 978 = 11110100102 = 11000203 = 331024 = 124035是最小的5-超级全数字数。
类似地，1093265784是最小的10-超级全数字数。
最小的10个10-超级全数字数之和为20319792309。
最小的10个12-超级全数字数之和是多少？