Ones in a Million

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

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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.