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# Summing a summed sequence

### #1

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.

### #2

Posted 10 July 2013 - 06:59 AM

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

- Bertrand Russell

### #3

Posted 10 July 2013 - 05:46 PM Best Answer

### #4

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

### #5

Posted 10 July 2013 - 06:35 PM

Spoiler for

i like this approach. What is your reasoning?

### #6

Posted 10 July 2013 - 06:35 PM

Spoiler for

is there another approach?

### #7

Posted 10 July 2013 - 08:09 PM

Spoiler fori like this approach. What is your reasoning?

### #8

Posted 10 July 2013 - 08:30 PM

### #9

Posted 10 July 2013 - 08:33 PM

Spoiler for My approach

i believe that this is the sum of a different sequence

### #10

Posted 10 July 2013 - 08:50 PM

i believe that this is the sum of a different sequenceSpoiler for My approach

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

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