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A little Help Needed !!

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, 4 months ago

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@Azhaghu Roopesh M Intelligent casework ;) Casework is an art ;) Pratik Shastri · 2 years, 4 months ago

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@Pratik Shastri Art In Smart xD Vraj Mehta · 2 years, 4 months ago

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@Pratik Shastri Yeah , agreed . Modern Art at that :P Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M True. Also, to improve upon your speed you may want to combine similar cases together. Pratik Shastri · 2 years, 4 months ago

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@Pratik Shastri 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 ? Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M Yeah I've read a bit about graph theory from that book of mine. Pratik Shastri · 2 years, 4 months ago

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@Pratik Shastri Ok , thanks . I had some doubts in it , I'll ask you afterwards . Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M 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. Raghav Vaidyanathan · 2 years, 4 months ago

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@Raghav Vaidyanathan 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 . Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M 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 Raghav Vaidyanathan · 2 years, 4 months ago

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@Raghav Vaidyanathan 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 ? Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M 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. Raghav Vaidyanathan · 2 years, 4 months ago

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@Raghav Vaidyanathan 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 ! Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M 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) Raghav Vaidyanathan · 2 years, 4 months ago

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@Raghav Vaidyanathan Also You may want to try this

Also You saw the Note On the extension for letter problem? Vraj Mehta · 2 years, 4 months ago

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@Vraj Mehta Is that your English notebook ? Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M Nope,My Physics Book Vraj Mehta · 2 years, 4 months ago

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Comment deleted Mar 05, 2015

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@Vraj Mehta no Raghav Vaidyanathan · 2 years, 4 months ago

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@Raghav Vaidyanathan Same here Misread the question Vraj Mehta · 2 years, 4 months ago

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@Vraj Mehta 92 dude !! Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M no Raghav Vaidyanathan · 2 years, 4 months ago

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@Raghav Vaidyanathan Oops! Misread your question ! You said two queens right ? I gave the answer for 2 . Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M @Azhaghu Roopesh M the problem i posed is a great example for your troubles. Raghav Vaidyanathan · 2 years, 4 months ago

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@Raghav Vaidyanathan Haha , look this up !

I agree on this , I'll start practicing these questions only from Monday onwards as far as Combinatorics is concerned . Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M I just remember Some part,Same question posted By @Roshan Shah Vraj Mehta · 2 years, 4 months ago

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@Vraj Mehta So , Physics over ? Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M Few Boring Chapters Left And Yourself? Vraj Mehta · 2 years, 4 months ago

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@Vraj Mehta Communication systems , and Electricity chapters revision left . And ofc , some derivations too ! Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M Also Make Intelligent Cases

Make your own patterns of identifying cases it will be better.. Vraj Mehta · 2 years, 4 months ago

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@Vraj Mehta Ok :) Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M Edit : 4 and 5 are The Same Questions Vraj Mehta · 2 years, 4 months ago

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@Vraj Mehta Oops , sorry ! Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M 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? Raghav Vaidyanathan · 2 years, 4 months ago

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@Raghav Vaidyanathan Actually I was going to see that only , I got the notification from the note by Deepanshu :) Azhaghu Roopesh M · 2 years, 4 months ago

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@Azhaghu Roopesh M @Azhaghu Roopesh M I have already solved two of the problems you have mentioned earlier. I can help you with them immediately! Raghav Vaidyanathan · 2 years, 4 months ago

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@Azhaghu Roopesh M Well I am weak in combinatorics. Hence I may be a little help of you. Ronak Agarwal · 2 years, 4 months ago

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