Summing digits to a million

What is the sum of all the digits of all the integers from 11 to 1,000,0001{,}000{,}000 inclusive? (For example, the number 4646 contributes 4+6=104 + 6 = 10.)

Show hints (2)+
  1. Pad numbers to 66 digits (000000000000–999999999999). In each position every digit 00–99 appears 100000100000 times.
  2. Per position: 100000⋅45100000\cdot45; times 66 positions; then add the digits of 1,000,0001{,}000{,}000.

Answer

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27000001

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