For https://twitter.com/ruanyf/status/1330340952590876672

cal.py

#!/usr/bin/env python
# Sat 21 Nov 2020 10:12:23 PM PST

def permutation(lst):
    assert len(lst) > 0
    result = []

    def helper():
        if len(lst) == 0:
            yield result[:]
            return
        for i in range(len(lst)):
            val = lst.pop(i)
            result.append(val)
            yield from helper()
            result.pop()
            lst.insert(i, val)
    yield from helper()

def check(lst):
    num = 0
    for i in range(len(lst)):
        num = num * 10 + lst[i]
    return num % (len(lst)) == 0

def merge(lst1, lst2):
    assert len(lst1) == len(lst2)
    result = []

    for i in range(len(lst1)):
        result.append(lst1[i])
        result.append(lst2[i])
    return result

def calculate():
    for evens in permutation([0, 2, 4, 6, 8]):
        for odds in permutation([1, 3, 5, 7, 9]):
            fail = False
            lst = merge(odds, evens)
            for i in range(1, len(lst) + 1):
                if not check(lst[:i]):
                    fail = True
                    break
            if not fail:
                print("".join(map(str, lst)))



if __name__ == '__main__':
    calculate()