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Challenge "Modular Sequences"

Challenge "Modular Sequences"  

  By: admin on Sept. 25, 2018, 2:19 p.m.

What do you know about modular sequences? Work it out.
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Re: Challenge  

  By: madness on Nov. 15, 2018, 3:25 a.m.

The answers to problem one are clear.
Problem two is worded strangely. I generated all 32 possible sequences, and there are 4 different periods. The "minimal" one is 1, as stated in the PDF. The server rejects all of them, however.

I am ready to give up. Will someone tell me the solution, so that I can understand what "for given initial values" means? In US English it means the values that have been given. It does not mean the same thing as "for arbitrary initial values".

Thanks

Re: Challenge  

  By: AnLeRo on Nov. 26, 2018, 10 p.m.

I have seen you solved the challenge in the meantime. Did you find out what "for given initial values" means and might it be interesting for other users?

Re: Challenge  

  By: Norbert on May 18, 2019, 9:32 p.m.

Did you find out what "for given initial values" means and might it be interesting for other users?

I read the 2nd problem as "what is the minimal period not equal to one for arbitrary initial values".

Re: Challenge  

  By: Hickman on May 20, 2019, 5:31 p.m.

Do you think it's possible that the wording is wrong in this one?

Re: Challenge  

  By: ancat on June 29, 2019, 11:32 a.m.

We replaced "for given initial values" by "for arbitrary initial
values".

Re: Challenge  

  By: Bart13 on July 16, 2019, 6:16 p.m.

We replaced "for given initial values" by "for arbitrary initial
values".

That was not really a big help. I still find the wording for Problem 2 extremely confusing.
Are you looking for one number or for a 'formula' containing S0-S5?
In the latter, the example for the solution is misleading.
In the former, which number has to be used as, and that has been mentioned before, there are several period lengths….

Please clarify the wording.

Re: Challenge  

  By: Luigy on Feb. 10, 2020, 1:23 a.m.

I don't understand problem 2 at all.

I have also already computed all the sequences for every one of the 64 possible combinations. I have used regex to look for the different periods and turns out only the 000000 has a period of 1 and all the others seem to have a period of the same exact number.
I am using this recurrence relation to solve:
si+6 = si + si+5 (mod 2),i > 0 ,

I don't even complain about the wording. This just doesn't make sense. The answer should be 1. If the initial values are arbitrary then there should be a way to compute this value with some kind of formula.

I am also finding it confusing some of you are talking about 32 combinations when in fact there are 2^6=64 combinations.

I wonder if that was your mistake and maybe the results i am having are the correct ones but the submission is not being the correct one.

Anyway… just venting and hope someone could help me out because i really don't see anything i am doing wrong.

Thanks

—————– EDIT ——————–

Ok i just got it and now i'm feeling silly and annoyed.

So the issue was that the problem 1 wants the actual sequence itself and not the length of the sequence. So i was bashing my head thinking problem 2 was incorrect when i had it hours ago and the issue was just the way to input the form.

[HTML_REMOVED]

I hope this helps others

Re: Challenge  

  By: tryone144 on Nov. 25, 2020, 2:29 p.m.

Hi glasshopper,

I see you solved the challenge in the meantime, but hopefully I can clarify some of the questions for future solvers.

s_0 to s_5 are the initial values for the sequence. To calculate the next value s_6 one uses the formula s_6 = (s_0 + s_5) % 2. Therefore, to calculate any later value s_i with i >= 6 the formula is s_i = (s_(i-6) + s_(i-1)) % 2 as you have correctly identified.

As the hint in the challenge suggests, you have to check the minimum period of all 2^6 possible combinations of the initial values s_0 to s_5. The solution for problem 2 is the minimum period length that holds for all those initial values.

Re: Challenge  

  By: itnomad on Jan. 18, 2021, 3:50 p.m.

Alright, in the first 5 or 6 tries I did it wrong for problem 1 as I forgot that the Fib-sequence starts with 0,1,1 - not 1,1,2. Doh. it's even written in the example.

But now that I think I did it right, I'm stuck with the minimum period as some other people. I can't seem to enter it right or I fundamentally misunderstood the task…

Re: Challenge  

  By: tryone144 on Jan. 18, 2021, 6:08 p.m.

Alright, in the first 5 or 6 tries I did it wrong for problem 1 as I forgot that the Fib-sequence starts with 0,1,1 - not 1,1,2. Doh. it's even written in the example.

Yep, problem one is one full period for the mod 3 and one for the mod 5 sequence starting with 0,1,1,…

But now that I think I did it right, I'm stuck with the minimum period as some other people. I can't seem to enter it right or I fundamentally misunderstood the task…

I can try to clarify my last post.
You have a recursive formula to calculate a sequence from 6 initial values (s_0 to s_5). Depending on these initial values, each sequence has a period with a specific length.
The answer to problem two is the minimum period length that holds true for all possible combinations of the inital values.

I.e. if one set of initial values has a period of length 5 and a second one has a period of length 3 the answer would be 15 (the least common multiple of 3 and 5).

I hope that helps with understanding what the expected answer for problem two is.


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