SOLUTION: All the positive integers with an initial digit of 2 are written down in succession. What is the 1978th digit thus written?

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Question 520170: All the positive integers with an initial digit of 2 are written down in succession. What is the 1978th digit thus written?
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

2 is the first one, then 20 through 29 are the next 10, then 200 through 299 are the next 100, then 2000 through 2999 are the next 1000. 1 + 10 + 100 + 1000 = 1111. 1978 minus 1111 is 867, so we need 867 more: 20000 through 20866 (only 866 because of zero based count)

John

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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
2 = 1 integer
20 - 29 = 10 integers
200 - 299 = 100 integers
2000 - 2999 = 1000 integers
So far:
+1+%2B+10+%2B+100+%2B+1000+=+1111+ integers
+1978+-+1111+=+867+
20000 - 20866 = 867 integers
The 1978th integer is 20866