Problem 42405. Divisible by 3

Created by goc3

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Pursuant to the <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42404-divisible-by-2">first problem</a> in this series, this one involves checking for divisibility by 3.Write a function to determine if a number is divisible by 3. This can be checked by at least two different methods:<ol><li>Sum the digits in the number. If the resulting sum is divisible by 3, then so is the original number. This routine can be applied recursively until the resulting sum is a single digit.</li><li>From the <a href = "https://en.wikipedia.org/wiki/Divisibility_rule">wikipedia reference page</a>: "Subtract the quantity of the digits 2, 5, and 8 in the number from the quantity of the digits 1, 4, and 7 in the number." If the resulting sum (absolute value) is a multiple of 3, then so is the original number.</li></ol>Previous problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42404-divisible-by-2">divisible by 2</a>. Next problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42406-divisible-by-4">divisible by 4</a>.

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Last Solution submitted on May 31, 2023

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Jean-Marie Sainthillier on 25 Jun 2015

I don't understand your restrictions. OK for Java functions, but here you need mod/rem no ?

goc3 on 25 Jun 2015

No, mod() or rem() isn't necessary because you can recursively apply the method, down to a single-digit number. The small number of single-digit numbers (i.e., 10, assuming absolute value) then makes checking against known divisible numbers trivial.

Alfonso Nieto-Castanon on 25 Jun 2015

I understand the java restriction, but the rest seem a bit heavy handed. Also the large number of similar problems might encourage solvers to build a general "divisible by n" routine instead

goc3 on 26 Jun 2015

I'm not trying to be authoritarian; just providing awareness to interesting mathematical trivia. There are some numbers, such as 7 and 11, for which a range of methods are possible. Without blocking a lot of those basic functions, very easy workarounds can be used, defeating the purpose of trying to optimize your score (akin to regexp, eval, etc. being banned due to defeating the scoring system).

goc3 on 26 Jun 2015

Also, building a general "divisible by n" routine is a good idea and I had thought about posting that at the end of the group of problems. I just think that it's too big for a standalone problem. There are many problems on Cody that are extremely simple and require no thought (like the recent string of beginner problems). There are also quite a few that require significant time, thought, and/or programming to solve, but they are all worth the same number of points. I prefer to break more difficult problems into simpler modules (just like is done in programming) to provide an encouraging approach, especially to those not already expert in Matlab. There are similarities between many of the problems in this set, but some numbers require quite different methods, such as 7 and 11.

Jan Orwat on 2 Jul 2015

Solved problems before reading comments and must agree with Alfonso. "divisible by N" approach worked nicely through all of them.

goc3 on 6 Jul 2015

Thanks for the comment. I'll be adding a few more problems to this set in the near future to round out and finish up the "divisible by N" approach.

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Problem 42405. Divisible by 3

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