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Champernowne Puzzle



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It's the same.


The number of digits in the first range is SUMn=[1,1180](9*10n-1*n) + 1181. 1180] into sub ranges based on the number of digits and call the number of digits n.

Let's break the range [1..10

For single digit numbers (n=1) the sub range is 1..9. There are 9 total digits.

For n=2, the sub range is 10-99. It contains 90*2 or 90*n digits.

For n=3, the sub range is 100-999. It contains 900*3 or 900*n digits

It's easy to see that for each sub range n the total number of digits is 9*n*10n-1

Adding up these sub ranges accounts for all except the last number, which has 1181 digits, so we need to add it to the sum.

Similarly, the number of zeroes in the second range is SUMn=[2,1181](9*10n-2*(n-1)) + 1181, so they are the same.

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