How many positive 10-digit integers of the form ABCDEFGHIJ, with non leading zeroes and each letter representing a different base 10 digit from 0 to 9, are divisible by 11,111 ?

Note : Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.

Onze=11111
Nbr=1000000000
# find first multiple of 11111
# ie increment NBr by 1 and stop when you have a multiple of 11111
# ie reminder of Nbr  didided by 11111=0
R=None
while R!=0:
    R=Nbr%Onze
    Nbr+=1
# FirstNbr is the first multiple of 11111 with 10 digits
CurrentMultiple=Nbr-1
print(CurrentMultiple)  # print first multiple
Solutions=[]        # make a list to store solutions
# now we will scan all multiples and see if they fulfill the ABCDEFGHIJ constraint
SolCount=0      # SolCount will count the solutions
while CurrentMultiple<10000000000:
    # check if all digits are differrebnt
    digits=set()    # create a python set to store digits
    for d in str(CurrentMultiple): # put all digits in the set"
        digits.add(d)
    if len(digits)==10: # if the length of the set is equal to 10, all digits are different
        SolCount+=1            # so we have a new solution
        Solutions.append(CurrentMultiple)
        print(CurrentMultiple)
    CurrentMultiple+=Onze
print(SolCount)    # print Count of Solutions
Solutions.sort()   # sort list of solutions
print(len(Solutions))
print(Solutions)    # print Solutions

Posted by jcbar on 2019-07-20 15:53:26