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Guest Message by DevFuse

# Summing a summed sequence

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Posted 10 July 2013 - 03:53 AM

using the sequence of numbers from 1 to 10,000, sum the digits together and rewrite the numbers as a new sequence.

For example:

......., 345, 346, 347, ....., 5088, 5089,

becomes

........., 12, 13, 14, ......, 21, 22

find a systematic approach or shortcut to adding the numbers from this second sequence without brute force calculations.

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### #2 bonanova

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Posted 10 July 2013 - 06:59 AM

Spoiler for Not sure this is what the OP asks, but ...

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #3 witzar

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Posted 10 July 2013 - 05:46 PM   Best Answer

Spoiler for

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Posted 10 July 2013 - 06:34 PM

Spoiler for Not sure this is what the OP asks, but ...

you are adding the actual numbers.  Like what Witzar did is what is asked for.  10,000 becomes 1 (since 1+0+0+0+0 = 1) and 9,999 becomes (36 since 9 +9 +9 +9 = 36) change all of the numbers in this manner, then add them up.

but rather then simply doing brute force calculations or using coding, how can we quickly find this solution

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Posted 10 July 2013 - 06:35 PM

Spoiler for

i like this approach.  What is your reasoning?

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Posted 10 July 2013 - 06:35 PM

Spoiler for

is there another approach?

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### #7 witzar

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Posted 10 July 2013 - 08:09 PM

Spoiler for

i like this approach.  What is your reasoning?

Spoiler for

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### #8 DeGe

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Posted 10 July 2013 - 08:30 PM

Spoiler for My approach

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Posted 10 July 2013 - 08:33 PM

Spoiler for My approach

i believe that this is the sum of a different sequence

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### #10 witzar

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Posted 10 July 2013 - 08:50 PM

Spoiler for My approach

i believe that this is the sum of a different sequence

The sequence is the same, but there is an error in reasoning.

Spoiler for error

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