Count F(n) - number of lucky tickets in range 1..n, the answer is F(b) - F(a-1). If n=4567, then F(4567) is number of 1-digit lucky numbers + number of 2-digit lucky numbers + number of 3-digit lucky numbers. With 4 digit numbers it's a bit harder - if first digit is 1..3, then remainder can be anything sustaining luckiness (i.e. there is no effect from upper border). Also first digit can't be 5,6,7. If first digit is 4, the last one can be anything except 4 - so you have multiplier 9 for the next step. This is not everything, but the basic idea.