What is the sum of digits in the numbers 1 to 2010?

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Discussion Overview

The discussion centers on calculating the sum of all the digits in the positive integers from 1 to 2010 inclusively. Participants explore different approaches and interpretations of the problem.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests a straightforward calculation of the sum of digits in the range.
  • Another participant humorously states "42" as the answer, referencing its cultural significance.
  • A third participant presents a formula, 2010*(2010+1)/2, which calculates the sum of all integers from 1 to 2010.
  • A subsequent reply questions the appropriateness of that formula, indicating it computes the sum of the numbers rather than the sum of the digits.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correct approach to the problem, with differing interpretations and methods presented.

Contextual Notes

The discussion does not clarify the method for calculating the sum of digits, and assumptions about the interpretation of the problem remain unresolved.

K Sengupta
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Determine the sum of all the digits in the positive integers from 1 to 2010 inclusively.
 
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42.

It's the answer to everything.
 
2010*(2010+1)/2
 
Wouldn't that get you the sum of all the numbers, not the sum of the digits?
 
0->9 : (0..9) = 45
10->19 : 10*1*(0..9) = 450
20->29 : 10*2*(0..9) = 900
30->39: 10*3*(0..9) = 1350
...
2000-2009 : 10*200*(0..9) = 90000

+ 1
...


10*(1..200) + 201*(0..9) + 1 = 201000 + 9045 + 1 = 210046 digits from 1 to 2010
 

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