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 $b$.
An $n$-super-pandigital number is a number that is simultaneously pandigital in all bases from $2$ to $n$ inclusively.
For example $978 = 1111010010_2 = 1100020_3 = 33102_4 = 12403_5$ 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?

Calculating the sum of the smallest $10$ $12$-super-pandigital numbers requires checking a large number of possibilities, so it might take some time.
Here’s a Python code that can be used to find the answer:

,,,,,,,,,,,,
def is_pandigital(n, base):
digits = set()
while n > 0:
digit = n % base
if digit in digits or digit >= base:
return False
digits.add(digit)
n //= base
return len(digits) == base

def find_smallest_super_pandigital(limit, num_bases):
n = 1
count = 0
while count < limit: if all(is_pandigital(n, base) for base in range(2, num_bases + 1)): count += 1 yield n n += 1 limit = 10 num_bases = 12 result = sum(find_smallest_super_pandigital(limit, num_bases)) print(result)

More Answers: