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# Hello Friends

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 $\huge \ddot\smile$

Note by Azhaghu Roopesh M
2 years, 2 months ago

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Guys , can you offer any help ? · 2 years, 2 months ago

Intelligent casework ;) Casework is an art ;) · 2 years, 2 months ago

Art In Smart xD · 2 years, 2 months ago

Yeah , agreed . Modern Art at that :P · 2 years, 2 months ago

True. Also, to improve upon your speed you may want to combine similar cases together. · 2 years, 2 months ago

Ok , then I'll try re-solving all the questions . Btw , do you know how to solve questions using Hamiltonian Paths , Markov Chains and Graph Theory ? · 2 years, 2 months ago

Yeah I've read a bit about graph theory from that book of mine. · 2 years, 2 months ago

Ok , thanks . I had some doubts in it , I'll ask you afterwards . · 2 years, 2 months ago

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. · 2 years, 2 months ago

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 . · 2 years, 2 months ago

The hydra question is one of the most beautiful questions that i have come across. I solved it while in kvpy camp... took me 10 mins. Asked Phd student same question, answer came in 10sec · 2 years, 2 months ago

So now you have seen the questions , no ? So how did you proceed with the Hydra ? What were your first thought for it? Did you use any advanced concepts ? · 2 years, 2 months ago

No, simple 12th standard probability. The answer came to me(actually, it is "us", me and my friend athul were independently solving the question) sooner than i expected. The basic idea is that u can form a cubic equation using recursive probability. Two line answer. The best 400 point problem ever. · 2 years, 2 months ago

Ok , but in general , is there any technique by which we can reduce or remove the casework that will be involved ?Like i said, generating functions can help sometimes , but other than that?

If no , then I guess,I better practice making cases ! · 2 years, 2 months ago

Depends on the problem, for example, in the archer problem, there is no other way to do it other than by taking cases. Some problems, if we are quick enough to figure it out, there may have workarounds for taking cases, for example, we may be ably to merge cases or take complement case(which may be easier to calculate). Otherwise, only resort is to meticulously calculate!

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) · 2 years, 2 months ago

Also You may want to try this

Also You saw the Note On the extension for letter problem? · 2 years, 2 months ago

Is that your English notebook ? · 2 years, 2 months ago

Nope,My Physics Book · 2 years, 2 months ago

Comment deleted Mar 05, 2015

no · 2 years, 2 months ago

Same here Misread the question · 2 years, 2 months ago

92 dude !! · 2 years, 2 months ago

no · 2 years, 2 months ago

Oops! Misread your question ! You said two queens right ? I gave the answer for 2 . · 2 years, 2 months ago

@Azhaghu Roopesh M the problem i posed is a great example for your troubles. · 2 years, 2 months ago

Haha , look this up !

I agree on this , I'll start practicing these questions only from Monday onwards as far as Combinatorics is concerned . · 2 years, 2 months ago

I just remember Some part,Same question posted By @Roshan Shah · 2 years, 2 months ago

So , Physics over ? · 2 years, 2 months ago

Few Boring Chapters Left And Yourself? · 2 years, 2 months ago

Communication systems , and Electricity chapters revision left . And ofc , some derivations too ! · 2 years, 2 months ago

Also Make Intelligent Cases

Make your own patterns of identifying cases it will be better.. · 2 years, 2 months ago

Ok :) · 2 years, 2 months ago

Edit : 4 and 5 are The Same Questions · 2 years, 2 months ago

Oops , sorry ! · 2 years, 2 months ago

I'll get back to you on those questions as soon as i can. Btw, I have posted a solution for this An algebra problem by rayyan shahid question. Can you see it it is right? · 2 years, 2 months ago

Actually I was going to see that only , I got the notification from the note by Deepanshu :) · 2 years, 2 months ago

@Azhaghu Roopesh M I have already solved two of the problems you have mentioned earlier. I can help you with them immediately! · 2 years, 2 months ago