# 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 \[\huge \ddot\smile\]

## Comments

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Guys , can you offer any help ? – Azhaghu Roopesh M · 2 years, 4 months ago

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– Pratik Shastri · 2 years, 4 months ago

Intelligent casework ;) Casework is an art ;)Log in to reply

– Vraj Mehta · 2 years, 4 months ago

Art In Smart xDLog in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

Yeah , agreed . Modern Art at that :PLog in to reply

– Pratik Shastri · 2 years, 4 months ago

True. Also, to improve upon your speed you may want to combine similar cases together.Log in to reply

– Azhaghu Roopesh M · 2 years, 4 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 ?Log in to reply

– Pratik Shastri · 2 years, 4 months ago

Yeah I've read a bit about graph theory from that book of mine.Log in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

Ok , thanks . I had some doubts in it , I'll ask you afterwards .Log in to reply

– Raghav Vaidyanathan · 2 years, 4 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.Log in to reply

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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– Raghav Vaidyanathan · 2 years, 4 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 10secLog in to reply

– Azhaghu Roopesh M · 2 years, 4 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 ?Log in to reply

– Raghav Vaidyanathan · 2 years, 4 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.Log in to reply

If no , then I guess,I better practice making cases ! – Azhaghu Roopesh M · 2 years, 4 months ago

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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) – Raghav Vaidyanathan · 2 years, 4 months ago

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this

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

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– Azhaghu Roopesh M · 2 years, 4 months ago

Is that your English notebook ?Log in to reply

– Vraj Mehta · 2 years, 4 months ago

Nope,My Physics BookLog in to reply

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– Raghav Vaidyanathan · 2 years, 4 months ago

noLog in to reply

– Vraj Mehta · 2 years, 4 months ago

Same here Misread the questionLog in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

92 dude !!Log in to reply

– Raghav Vaidyanathan · 2 years, 4 months ago

noLog in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

Oops! Misread your question ! You said two queens right ? I gave the answer for 2 .Log in to reply

@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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this up !

Haha , lookI 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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@Roshan Shah – Vraj Mehta · 2 years, 4 months ago

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

– Azhaghu Roopesh M · 2 years, 4 months ago

So , Physics over ?Log in to reply

– Vraj Mehta · 2 years, 4 months ago

Few Boring Chapters Left And Yourself?Log in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

Communication systems , and Electricity chapters revision left . And ofc , some derivations too !Log in to reply

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

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– Azhaghu Roopesh M · 2 years, 4 months ago

Ok :)Log in to reply

– Vraj Mehta · 2 years, 4 months ago

Edit : 4 and 5 are The Same QuestionsLog in to reply

– Azhaghu Roopesh M · 2 years, 4 months ago

Oops , sorry !Log in to reply

An algebra problem by rayyan shahid question. Can you see it it is right? – Raghav Vaidyanathan · 2 years, 4 months ago

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

– Azhaghu Roopesh M · 2 years, 4 months ago

Actually I was going to see that only , I got the notification from the note by Deepanshu :)Log in to reply

@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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– Ronak Agarwal · 2 years, 4 months ago

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