I have been facing a difficulty for quite some time now . Whenever I am solving a good Combinatorics Question which involves casework , my imagination runs dry(it has happened 3-4 times already in the last few days) and I end up losing out on some cases , thus getting the question wrong .

Can anyone suggest any alternative to making cases ? Well you could generate a function for some easy questions but what about the rest ?

Is there any standard procedure for making cases , which I am not aware of ? If so please enlighten me on it !!!

Any help in this regard will be appreciated !

Thanks for the same \[\huge \ddot\smile\]

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## Comments

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Guys , can you offer any help ?

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Intelligent casework ;) Casework is an art ;)

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Art In Smart xD

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Yeah , agreed . Modern Art at that :P

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Can you give an example of where you face problems? Maybe then it would be easier to help you out. In a lot of cases, taking the complement case is easier.

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Actually yes , there are a certain questions .

1 , 2 , 3 and 4 . You might be wondering how I solved those questions , since you may see that I am the last solver of the first two questions , but let me tell you that I had taken help from some teachers from my Coaching Institute . Now , I am not able to recall the exact method that I had used back then , but if I am able to derive or create a new method for solving instead of making cases , it'll surely save a lot of time .

All the solutions that have been posted have used extensive casework ,which really is not my forte .

P.S. I do think that there are some other questions , but I don't remember their names .

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If no , then I guess,I better practice making cases !

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Do this as practice: Find number of ways of placing two queens on a 8x8 chessboard, such that they dont take each other on. (They don't attack each other)

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this

Also You may want to tryAlso You saw the Note On the extension for letter problem?

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Comment deleted Mar 05, 2015

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@Azhaghu Roopesh M the problem i posed is a great example for your troubles.

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this up !

Haha , lookI agree on this , I'll start practicing these questions only from Monday onwards as far as Combinatorics is concerned .

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@Roshan Shah

I just remember Some part,Same question posted ByLog in to reply

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Make your own patterns of identifying cases it will be better..

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An algebra problem by rayyan shahid question. Can you see it it is right?

I'll get back to you on those questions as soon as i can. Btw, I have posted a solution for thisLog in to reply

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@Azhaghu Roopesh M I have already solved two of the problems you have mentioned earlier. I can help you with them immediately!

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Well I am weak in combinatorics. Hence I may be a little help of you.

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