#!/usr/bin/env python3 def search(i, k, fst, dig=None, r=0, num=str()): if dig == None: dig = fst if i == 0: return False n = k*dig + r if n < 10 and fst == n and dig != 0: return str(dig) + num return search(i-1, k, fst, n%10, n//10, str(dig) + num) places = 100 s = 0 for k in range(1, 10): for dig in range(1, 10): n = search(places, k, dig) if n: r = places // len(n) for i in range((1 + (len(n)==1)), r+1): s += int(i*n) % 10**5 print(s % 10**5)