ASCII value gets you out of trouble

Level 3

Evaluate

a = 0 b = 0 c = 0 a d = 0 b e = 0 d ( n + a a ) ( b e d e ) ( a c ) ( b e ) ( 1 ) b + c n e c d e \sum_{a=0}^\infty \sum_{b=0}^\infty \sum_{c=0}^a \sum_{d=0}^b \sum_{e=0}^d {n+a \choose a} {b-e \choose d-e} {a \choose c} {b \choose e} (-1)^{b+c} n^e c^{d-e}

Now before you enter your final answer -

If your final answer is a rational number and is in the form p q \frac{p}{q} where p p and q q are coprime to each other then your final answer should be p π q \frac{p\pi}{q} .

Otherwise If your final answer is an irrational number then your final answer should be 99 99

It is an entry in the Troll King Contest.


The answer is 3.

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1 solution

Kishlaya Jaiswal
Mar 21, 2015

No need to evaluate that dirty sum. Ok, read below to know why.

We are being provided with two situations -

If our finals answer is rational number then our final answer becomes p π q \frac{p\pi}{q} . But now notice that it becomes an irrational number. So basically, we need to jump to the second condition which says that now our final answer becomes 99 99 which is indeed a rational number.

Hence, we are kinda stuck in an Infinite Loop .

And the same happens if you got an irrational number as the value of the sum.

Now, we aren't working on a console so that we can press Ctrl+C to exit this loop. So we want Brilliant to somehow exit us out of this loop and therefore, our answer should be something like to get out of this infinite loop.

Also, we know that Brilliant accepts only integers answers unless and until there is another note attached to it which says "decimals OK". So which now want some means to interpret Ctrl+C as an integer value.

So, what's the best option in this case?

Yeah, you got it right. ASCII value (as the title says) of Ctrl+C which is perhaps 3 \boxed{3}

And to all those friends who tried trolling with that sum, the answer of that sum is 1 . I'll soon post a note to explain it why. So, infact this problem will also serve the purpose of explaining multiple sums to my friends who requested it - Azhaghu Roopesh M megh choksi and all others.

Phew ! at last , I got it on my third try .

Nice job on the trolling Kishlaya .

You got me twice . I had entered the ASCII values for "C" and "c" , frankly I had never thought that one existed for "Ctrl+C" .

And yeah , looking forward for your note :)

A Former Brilliant Member - 6 years, 2 months ago

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Awesome, well done!

Actually, looking at the stats of this problem, I believe no one is even attempting the problem because of that dirty sum. Seriously, it's #super_troll

Kishlaya Jaiswal - 6 years, 2 months ago

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Lol . #super_troll . Yup it is!

So are your revisions for JEE done ? My class XI Physics is left (some chapters)

A Former Brilliant Member - 6 years, 2 months ago

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@A Former Brilliant Member Lol, I have still complete Chemistry left. No matter how much I study that subject, it keeps trolling me everyday, all time.

Kishlaya Jaiswal - 6 years, 2 months ago

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@Kishlaya Jaiswal Haha , please don't joke . I remember that you had said you will be revising Chem during the last few days .How can you revise without first not studying it ?

A Former Brilliant Member - 6 years, 2 months ago

Was nice, I didn't even try due to the threatening sum.. :D

Rishabh Tripathi - 6 years, 2 months ago

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Well, if you want to see a solution to that threatening sum, then you can check my latest note.

Kishlaya Jaiswal - 6 years, 2 months ago

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its out of my understanding, I've just started with basic summations

Rishabh Tripathi - 6 years, 2 months ago

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@Rishabh Tripathi No worries.

You can read the Summations wiki, and the Infinite Sums wiki to get a basic understanding.

Kishlaya Jaiswal - 6 years, 2 months ago

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@Kishlaya Jaiswal I'll do it.. thank you.

Rishabh Tripathi - 6 years, 2 months ago

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