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Related: Culture Forums, Support ForumsNeed some math confirmation from a math whiz - 3 series of numbers
Series A is 1, 2, 3, 4... 28
Series B is 1, 2, 3, 4... 34
Series C is 1, 2, 3, 4... 80
If each series starts at 1 and continually repeats itself, how many times through Series A will it be until all three series' are at "1" again at the same time? (meaning, Series A resets back to "1" when Series B and C are at "29", and then Series B resets to "1" when Series C is at "35" and Series A is now on "6"
As a second challenge, when does each series' halfway point coincide? Meaning, when is Series A at "14" while Series B is at "17" and Series C is at "40" ?
For the first problem, I came up with 340 times through Series A, with "1" coming up at the beginning of the 341st time through Series A. Is there an easy way to calculate? (I did it by copying & pasting in Excel and some IF statements)
I haven't calculated the second part yet.
Thanks a lot
Baitball Blogger
(46,758 posts)Let me know when I can highlight the white for the answer.
NewJeffCT
(56,829 posts)I'm trying to come up with the answer myself.
ret5hd
(20,523 posts)For the halfway point, maybe some fraction or root of the lowest common multiple.
if you take 14, 17 and 40 and multiply them, you get 9,520. 9,520/28 is 340
pokerfan
(27,677 posts)by taking the LCM of 28, 34 and 80, then dividing by 28.
For the second problem, I would probably start with taking the LCM of 14, 34 and 40, then discarding the solutions that have even number of cycles as only the odd ones would represent halfway points.
I'll see what I can come up with for the second part as well.
struggle4progress
(118,356 posts)Solutions occur whenever a = 17*20*n = 340*n, b = 14*20*n = 280*n, c = 7*17*n = 119*n due to the fact that
28*17*20 = 14*34*20 = 7*17*80
For the second part, I think you may need to find an odd number that is even
NewJeffCT
(56,829 posts)And, for the second part, I figured if you went through the series enough times, you might be able to have them at the halfway point together at some time.
struggle4progress
(118,356 posts)which corresponds to passing "a and a half times" thru the first series, "b and a half times" thru the second series, and "c and a half times" thru the third series
For more info, look up the "Chinese Remainder Theorem"