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How many 1s? (Posted on 2004-07-26) Difficulty: 2 of 5
If I took all the numbers from one to one billion:
  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?

See The Solution Submitted by Thalamus    
Rating: 3.0000 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solutions | Comment 3 of 16 |
(In reply to Solutions by Federico Kereki)

The fraction of numbers in the range 000,000,000 to 999,999,999 that do not have a 1 in any position can be calculated as .9^9.  So the number that do have at least one 1 number 1,000,000,000*(1-.9^9), and then add 1 for 1,000,000,000.  This agrees with Federico's summation and with Penny's result: 612,579,512.

 


  Posted by Charlie on 2004-07-26 10:50:27
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