Talk:Kaprekar numbers: Difference between revisions
(→Why the complexity?: Because of the inclusion of 1 in the series.) |
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The wikipedia page says "Let X be a non-negative integer. X is a Kaprekar number for base b if there exist non-negative integers n, A, and positive number B satisfying ...". In other words A can be zero. Why do we have to have a bunch of text claiming that A cannot be zero but A can be an empty string and that it is meaningful to add an empty string to a number? (Can't we just take advantage of the fact that leading zero digits do not change the value of a number?) --[[User:Rdm|Rdm]] 20:56, 7 June 2011 (UTC) |
The wikipedia page says "Let X be a non-negative integer. X is a Kaprekar number for base b if there exist non-negative integers n, A, and positive number B satisfying ...". In other words A can be zero. Why do we have to have a bunch of text claiming that A cannot be zero but A can be an empty string and that it is meaningful to add an empty string to a number? (Can't we just take advantage of the fact that leading zero digits do not change the value of a number?) --[[User:Rdm|Rdm]] 20:56, 7 June 2011 (UTC) |
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:To me the text "However a conceptual single split at the very end or before the first digit that produces one empty string does have the empty string counted" means that A can be zero. Unless I'm confused about what A and B are. --[[User:Mwn3d|Mwn3d]] 22:30, 7 June 2011 (UTC) |
:To me the text "However a conceptual single split at the very end or before the first digit that produces one empty string does have the empty string counted" means that A can be zero. Unless I'm confused about what A and B are. --[[User:Mwn3d|Mwn3d]] 22:30, 7 June 2011 (UTC) |
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Consider 100*100 = 10000 which could be split as 100 + 00. Now the 00 is ''dis''allowed. |
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Compare that with 1*1 = 1 which ''is'' a K-number. For this to be a k-number then it must be expressed as either 1 plus no digists to the right or no digits to the left + 1. Either way no digits is treated as a positive integer of value zero but any string of one or more noughts is expressly forbidden. |
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Having 1 in the series seemed to add that complexity that needed explaining in my mind. --[[User:Paddy3118|Paddy3118]] 23:14, 7 June 2011 (UTC) |
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Revision as of 23:14, 7 June 2011
Java count missing
Just add (and show), the count of how many there are <1million and you will have completed the stretch goal! --Paddy3118 14:07, 7 June 2011 (UTC)
- I had actually added it as a test because I saw the other examples do it, but for some reason I didn't read it as a requirement so I took it out. Mornings are hard. --Mwn3d 14:47, 7 June 2011 (UTC)
- :-)
--Paddy3118 17:29, 7 June 2011 (UTC)
- :-)
Why the complexity?
The wikipedia page says "Let X be a non-negative integer. X is a Kaprekar number for base b if there exist non-negative integers n, A, and positive number B satisfying ...". In other words A can be zero. Why do we have to have a bunch of text claiming that A cannot be zero but A can be an empty string and that it is meaningful to add an empty string to a number? (Can't we just take advantage of the fact that leading zero digits do not change the value of a number?) --Rdm 20:56, 7 June 2011 (UTC)
- To me the text "However a conceptual single split at the very end or before the first digit that produces one empty string does have the empty string counted" means that A can be zero. Unless I'm confused about what A and B are. --Mwn3d 22:30, 7 June 2011 (UTC)
Consider 100*100 = 10000 which could be split as 100 + 00. Now the 00 is disallowed. Compare that with 1*1 = 1 which is a K-number. For this to be a k-number then it must be expressed as either 1 plus no digists to the right or no digits to the left + 1. Either way no digits is treated as a positive integer of value zero but any string of one or more noughts is expressly forbidden.
Having 1 in the series seemed to add that complexity that needed explaining in my mind. --Paddy3118 23:14, 7 June 2011 (UTC)