> I want to improve my skill but I don't feel like I should pick up advanced algebra or number theory just to do a coding assignment.
Really? Advanced algebra or number theory? Can you show me a coding assignment that required either? Are you sure you're not just excusing your ignorance by suggesting that stuff you've been asked and didn't know the answer to is somehow advanced when it's really not?
An integer partition of a number n is a way of writing n as a sum of positive integers.
Partitions that differ only in the order of their summands are considered the same. A partition of n into distinct parts is a partition of n in which every part occurs at most once.
The partitions of 5 into distinct parts are: 5, 4+1 and 3+2.
Let f(n) be the maximum product of the parts of any such partition of n into distinct parts and let m(n) be the number of elements of any such partition of n with that product.
So f(5)=6 and m(5)=2.
For n=10 the partition with the largest product is 10=2+3+5, which gives f(10)=30 and m(10)=3. And their product, f(10)·m(10) = 30·3 = 90
It can be verified that ∑f(n)·m(n) for 1 ≤ n ≤ 100 = 1683550844462.
Find ∑f(n)·m(n) for 1 ≤ n ≤ 1014. Give your answer modulo 982451653, the 50 millionth prime.
Can they start picking it apart, and at least find some bits of it they can solve, or do they squirm, or whine, or rage quit?
Attacking ridiculously hard requirements is a valuable skill even in crud jobs.
No - it's about about people. And helping them solve their real problems.
Math is just a means to that end (one among many).
The question "why are so many coding challenges about maths?" You answer is "it's about the people."
... what?
-- "Because that's where the light is."
Less snarkily: that's because they traits that really matter in a modern development environment -- the ability to deal with ambiguity and complexity; to navigate the tipping points between technical perfection and optimal business value; and and top of all this, a genuine sense of humility and a willingness to work with others whose strengths and weaknesses are different from your own -- are very hard to test for, if they can be "tested" for at all.
But since the current interview "process" is so obsessed with "testing" and stack-ranking... not surprisingly, it's largely rigged around traits that are... easy to "test" for.
Like you know, the ability to crank out rehearsed solutions to algorithm puzzles and the like.
That being said, most of the coding I've done in my life has been all about integrating different libraries and frameworks together. I don't see a lot of complex algorithms, which is good (because they are complex, and probably someone else already wrote it better, with less bugs and better performance). I'd never want to work with someone who rolls their own red black tree into production code just for the lols.
That being said, I don't think it's a great way to evaluate candidates, because it's not what most people do all day. I find problems about integrating systems, and understanding complex topics like networking, databases, testing, protocols, and APIs to be much more useful.
To find a good middle ground, I like to ask design questions, and then give people a "library" of functions they can call with prototypes, and tell them what they will do. This focuses on the logic of putting it together rather than off by one errors in loops, which still happens to me all the time. Those kinds of bugs are easy to fix when you can actually run the code, but a right pain on a whiteboard.
I'll never forget the look of surprise on the interviewers face when I was doing an intern interview and asked "can I use stdlib calls like memset and memcpy, or do you want me to write loops?" I think just asking the question gave me huge interview points. (and yes, I got the job.)
Let me finish by giving an example of what I thought was a good coding assignment: Write a service that listens to rabbitmq and rotates the images 90 degrees and post them back to a different queue. This wasn't about writing code to rotate images either, it was about knowing how things work, and stitching them together correctly (with the right error handling and failure modes).
IMO this is horribly broken but the Big 4 do it so everyone else does too.
https://www.hackerrank.com/calendar
I think topcoder (https://www.topcoder.com) covers a wide spectrum, but i have never tried them.
2. As stated in earlier comments, because mathematics is unambiguous making the problem easy to state and easy to verify. Can you take a small piece of mathematics you may not be familiar with, understand it and translate that into working code? That is a core skill of any software developer -- not necessarily with just mathematics but you get the point.
