A few days ago i stumbeld upon a 1200 which gave me a headache 1822D - Super-Permutation , and just now i solved it. What i want you to do is look at this problem and try figuring it out , then read the rest of this post.

The way i solved it , and what i believe to be the easiest way of solving it looking at last test case and finding the pattern, after this you should be all set , the implementation is really easy.

This problem taught me that i really need to observe the test cases more , even if there is really only one useful test case.

Enjoy the rest of your day.

For such questions i generally write brute force and observe the pattern like here it was n 1 n-2 3.... and so on

Oh , that also works? I used n,n-1,1,n-3,3,...

A very similar problem appeared on the Junior Bosnian Mathematical Olympiad. link

Translation:

Let $$$n$$$ be a natural number and let $$$a_1, a_2, ... , a_n$$$ be natural numbers from the set $$$(1,2,...,n)$$$, where each one of those numbers appears exactly once. Is it possible that the numbers $$$a_1, a_1 + a_2, ..., a_1 + a_2 + ... a_n$$$ all have different residues upon division with $$$n$$$ if: a) $$$n = 7$$$; b) $$$n = 8$$$?

I do agree observation is important in many cases. However, I don't think you should consider a constructive problem "observation" or "finding the pattern" when you can't solve it; In fact, I think the other situation is you're not familiar with something related to the problem. (At least, I don't think the problem you mentioned above is all about observation, for I've come up with the construction almost instantly without looking around for too much, so maybe you're just not familiar with the nature of permutation and modulars)

Anyway, good luck on practising your observation skills XD

Thanks XD

My brother in christ. This is not what people mean with "make observations about the problem".

https://mirror.codeforces.com/blog/entry/106346

nicely explained , i have one question ,how to come up observations faster? i go through the same process you mentioned to solve problems, but the thing is i am very slow, also it's not like i lack practice in this method or anything. the chain of reasoning you mentioned ,, it takes me lot of time to go through that and arrive at useful observations about the problem and by that time the contest is over.

That's not an observation. It's a hack for sometimes solving problems in a contest. It's a useful hack and is also a way of ACing the problem but you can't put every constructive problem in the same category. (as many problems have multiple valid outputs)

Thanks for educating us