## 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:

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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)

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