Of the integers from 1 to 1,000,000, which are more numerous: the numbers that contain a 1 or those that don’t?

To list the numbers that don’t contain a 1, imagine six spaces and fill each with the digits 0, 2, 3, 4, 5, 6, 7, 8, or 9. The number of ways of doing this is 96. There’s one exception: 000000 doesn’t fall between 1 and 1,000,000. So the number of integers without 1 is 96 – 1 = 531,440, and the number with 1 is 468,560.