Some techniques I learnt recently.

 Hello ! It's a loooooong time since I posted, actually I posted only once tho before this :P. 

I have been doing a lot of combo problems recently, and this post will have some tricks which I learnt while trying the problems, and you can think of it while trying other problems if you get some intuition or so. Another reason why I am writing this is like I think of the idea, but I tend to think it's useless (while solving the prob) and many a times, the same idea is used in some solution to the problem which I discarded. So, I hope you won't do the same mistake :D. 

Let's start 😁

(1) Think about base cases. So if a problem asks you to show something is true for n, think what will happen if -> n = 2,3,4,5. Maybe you can take some more base cases to think if that is possible with time constraints. 

(2) If the problem is related to ordering or something, take a small n, say n = 4 or 5, and try to think of various permutations and the "ideal" strategy of what you are going to do in such a case, as you can guess most of the times what the strategy is from small cases and they are a bit easier to handle too. e.g. EGMO 2018/3 . Part (a) of this is a nice example of what I wany to say.

(3) Thinking of what maximum or minimum element is in a given configuration is helpful too . e.g.  USACO feb 2018/3 , it was done by L567 and biomathematics and I was just spectating, but I learnt to use this new idea :P

(4) Suppose you have to prove that something is false, you can think what will happen in the problem if it is true, and get some structure and prove that the given statement is not true in the structure you obtained. One example of this is Russia 2004 Grade 9, P1 . I'll post my solution to this problem with this idea in my blogpost soon :P 

(5) In 2 player games question, you can actually play the game for some time say 5-7 minutes and get the idea of what winning "configurations" are and then trying to prove it. An example of which is RMM 2019/1 . I'll post the solution of this problem too soon.

I can't recall any other techniques as of now, I'll add some if I recall or learn new techniques :D. I hope this post was helpful! Thanks for reading it so far. Happy problem solving !

P.S. :- For reference/further reading, I think evan's post on Hard and soft techniques would be perfect !.