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The sum of all the digits used to write the whole numbers 10 through 13 is 1+0+1+1+1+2+1+3 = 10. What is the sum of all the digits used to write the whole numbers 1 through 100, inclusive?

 Jun 27, 2020
 #1
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The sum of all digits: 1 + 2+ 3 +4..........9 + 9 +9 +1 +0 +0+ 0=13,501 - which includes both 1 and 1000.

 Jun 27, 2020
 #2
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The sum of the digits used to write the whole numbers 1 through 100 (inclusive):

 

First, the units digits:   1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9  =  45

These units digits will be repeated for each of the sets: 10 ... 19, 20 ... 29, 30 ... 39, ..., 90 ... 99

So the total of the units digits is 10 x 45 = 450 

 

Now, the tens digits:

--  in writing the numbers from 10 through 19 the "1" will be written 10 times:  10 x 1  =  10

--  in writing the numbers from 20 through 29 the "2" will be written 10 times:  10 x 2  =  20

--  in writing the numbers from 30 through 39 the "3" will be written 10 times:  10 x 3  =  30

So, we also have 10 x 4 = 40, 10 x 5 = 50, 10 x 6 = 60, 10 x 7 = 70, 10 x 8 = 80, and 10 x 9 = 90

Summing the tens digits:  450.

 

Total for both the ones digits and the tens digits = 900

 

Plus the "1" in 100:  901.

 Jun 27, 2020

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