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Steve Hewson
Frequent poster

Post Number: 192
 Posted on Wednesday, 16 January, 2013 - 06:36 pm:

I've made a new area on the NRICH website where people can send in investigations and explorations that they have done so that a) their efforts can be celebrated and b) so that a community of ideas can develop in a similar way to that of the research mathematics community where ideas are posted and developed in collaborative way.

Anyway, the first such investigation has now appeared. Please feel free to read it, take a look and extend or comment. Please do so in a kind and supportive way :-)

Steve (The NRICH Post-16 person)
azerbajdzan
Veteran poster

Post Number: 1360
 Posted on Thursday, 17 January, 2013 - 11:41 pm:

It can be generalized to any number, not requiring ascending order of digits of numbers.

For example:
41651627

+{41651627, 16516274, 65162741, 51627416, 16274165, 62741651,27416516, 74165162}
-{16516274,65162741,51627416,16274165,62741651,27416516,74165162,41651627}
={25135353,-48646467,13535325,35353251,-46467486,35325135,-46748646,32513535}

In the result all positive numbers are "cyclic" and all negative numbers are "cyclic".
{25135353,13535325,35353251,35325135,32513535}
{-48646467,-46467486,-46748646}

The requirement of ascending digits produces only positive numbers (except the last number) making it a special case of the above generalization.

Also notice that for n-digit number I used all n cycles, while author uses only n-1 cycles.
Abhay Rangan
New poster

Post Number: 1
 Posted on Saturday, 19 January, 2013 - 05:43 pm:

Note: In the second example where I use 124 to explain the Theory of Cycles, the diagram shows 123. Please forgive the error.
Abhay Rangan
New poster

Post Number: 2
 Posted on Friday, 25 January, 2013 - 03:13 am:

Problem solved. The corrected pdf is uploaded in place of the first one.

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