1. How many of them contain at least one '1'?
2. If I wrote them out in one long line, how many 1 digits would there be?

N(x) = number of numbers <1 billion that satisfy condition x

N(at least 1) = 1 billion - N(no ones)

                   = 1billion  - 9^9

                  = 612 579 511

9^8 contain 1 one

9^7 contain 2 ones

9^6 contains 3 ones

9^5 contains 4 ones

9^4 contains 5 ones

9^3 contain 6 ones

9^2 contains 7 ones

9 contain 8 ones

1 contains 9 ones

=3 868 151 445 without counting 1 billion

=3 868 151 446 if you include 1 billion

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