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If only the positive integers from 1 through 49, inclusive, are written on a piece of paper, how many times is the digit 1 written?

 Apr 16, 2021
 #1
avatar+33620 
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1   10    11   21   31   41     12   13   14   15   16   17  18  19       15 times

 Apr 16, 2021
 #2
avatar+180 
+1

We can start with cases

 

Case 1: How many of the one digit numbers have the digit 1? We easily know that there is only 1

 

Case 2: How many of the digit one is written from 10-19? We count that there are 10 digit ones in the first digit and one digit in the last digit. This gives us 11 digit 1 written.

 

Case 3: How many of the digit one is written from 20-49. There is only three which is 21, 31, and 41.

 

This gives us the total of 15 digit one written.

 

Hope this helped! laugh

 Apr 16, 2021

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