Talk:Casting out nines

I am trying to understand this task.

Would it be fair to change the final sentence to read:

The task is to write code that given a numeric base and two numbers that mark the begining and end of a range use only this test to eliminate numbers from the range which cannot be valid Kaprekar numbers -- the result is the rest of the numbers from that range.

Or have I completely misunderstood what you are trying to convey?

--Rdm 13:59, 25 June 2012 (UTC)

OK, you have not misunderstood what I am trying to convey. I wanted to accept any test based on the congruence B^n=1(mod B-1). The Kaprekar numbers are a good objective because they have the property k%(B-1) == (k*k)%(B-1) and are explained elswhere on this site. I would accept any other objective.

Ok! I think the current task description is a bit too coy about the filtering mechanism. It's almost equivalent to "filter numbers" since the description of the selection function is so general. I am currently thinking it should be:

Given two numbers which mark the beginning and end of a range of integers [LO,HI], and an integer base (BASE), return the integers which fall in that range where the remainder after dividing the number by BASE-1 is the same as the remainder after dividing the square of the number by BASE-1.

That is the test, but I also want to keep the explanation of why we are doing this. Note that Ledrug has implemented the test as ((k*k) - k)%(Base - 1) at http://rosettacode.org/wiki/Kaprekar_numbers#C which is another variation. --Nigel Galloway 13:03, 27 June 2012 (UTC)

--Rdm 14:02, 26 June 2012 (UTC)

I'd like to see a different title for the task. The current description states right up front that the task is not casting out nines. —Sonia 19:46, 26 June 2012 (UTC)

OK, maybe you have misunderstood what I am trying to convey. Following Dr. Math at http://mathforum.org/library/drmath/view/55926.html describing casting out nines to the phrase "(You wouldn't normally get the same check digit for the result of the sum and the products; I just picked a weird example.)" I see that every Kaprekar is a "weird example". Using Dr. Maths "quick explanation of how to do it, without the big words" would be as slow as the String C++ Kaprekar solution. So we turn to http://mathworld.wolfram.com/CastingOutNines.html. What is said there is true for bases other than 10, therefore it is possible to develop a fast test. --Nigel Galloway 12:47, 27 June 2012 (UTC)

(Comments moved from task page following Go solution.) I'm not seeing the connection. —User:Sonia

If you replace the line if k%(base-1) == (k*k)%(base-1) { with something like if co9Peterson(k) == co9Peterson(k*k) { in the C++ translation would it not solve the task? Obviously as written you would have to change k and k*k to strings and it would only work base10, but I think you have demonstrated the connection.--Nigel Galloway 15:15, 28 June 2012 (UTC)

Done. Posted now are my two Go solutions combined, generalized to other bases, and then modified to demonstrate what the task seems to be asking for. I do think that people will protest that my casting out nines code is superfluous, and I will then repeat that the task should not be called casting out nines if nothing in the task is casting out nines. —Sonia 19:20, 28 June 2012 (UTC)

Agreed. I've changed the task description, do you prefer it? People should not now protest that your casting out of nine is superfluous. It has made it longer, so they may not thank you either. --Nigel Galloway 12:32, 29 June 2012 (UTC)