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Topic: What am I doing? (Read 520 times) |
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Leo Broukhis
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What am I doing?
« on: May 15th, 2003, 9:01am » |
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I have a very long positive integer number, written in decimal.
I take its last (least significant) digit, multiply it by 9 and add to the number
formed by the remaining digits (e.g. 9999 -> 999 + 9*9 = 1080 -> 108 + 0*9 = 108 -> 10 + 8*9 = 82) until the result is less than 100.
By looking at the result I can find something out about the original number. What is that property of the original number?
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wowbagger
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Re: What am I doing?
« Reply #1 on: May 15th, 2003, 9:21am » |
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If you subtracted nine times the last digits from the rest, I'd know the answer.
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| « Last Edit: May 15th, 2003, 9:21am by wowbagger » |
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Leo Broukhis
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Re: What am I doing?
« Reply #2 on: May 15th, 2003, 10:20am » |
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on May 15th, 2003, 9:21am, wowbagger wrote:| If you subtracted nine times the last digits from the rest, I'd know the answer. |
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And it would be different from what I had in mind. But, I believe, you're thinking in the right direction.
Hint: what's the fixed point of the transform?
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Lightboxes
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Re: What am I doing?
« Reply #3 on: May 15th, 2003, 5:15pm » |
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Are we allowed to know the original number AND the result
OR just the result and then we have to guess the orginal number's property?
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Leo Broukhis
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Re: What am I doing?
« Reply #4 on: May 15th, 2003, 5:50pm » |
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on May 15th, 2003, 5:15pm, Lightboxes wrote:Are we allowed to know the original number AND the result
OR just the result and then we have to guess the orginal number's property?
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For the sake of the puzzle, let's say that you're only allowed to know the result. Knowing that it was achieved by the transform in question, what is the property of the original number (and all intermediate results as well, of course) that you can assert?
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wowbagger
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Re: What am I doing?
« Reply #6 on: May 16th, 2003, 2:28am » |
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on May 16th, 2003, 12:11am, Lightboxes wrote:| There is also another pattern of +/- of 89 between possibilities. |
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That's the right track.
Now, what property of a number could this be connected with?
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| « Last Edit: May 16th, 2003, 2:28am by wowbagger » |
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Lightboxes
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Re: What am I doing?
« Reply #7 on: May 16th, 2003, 11:46am » |
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If (R*10)>=100 then R=N;
(N*10)-89=N for N>=100
This equation will give you all the possible intermediate and orginal numbers by using it again and again on the numbers that are created from the first step.
89 is also a prime number. Am I closer?
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James Fingas
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Re: What am I doing?
« Reply #8 on: May 16th, 2003, 12:34pm » |
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Uneducated guess: probably deciding whether or not a number is divisible by 89 I know that 89 is unaffected by the transform...
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Leo Broukhis
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Re: What am I doing?
« Reply #9 on: May 16th, 2003, 3:04pm » |
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The "uneducated" guess is, nevertheless, correct.
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