
Three Puzzles Inspired by Ramanujan - aburan28
https://www.quantamagazine.org/20160714-three-puzzles-inspired-by-ramanujan/
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SilasX
Mind blown: The article made me realize that you can generate one of those
trippy "continued fraction" equalities any time you have x on both sides of
the equation, one side by itself.

Golden ratio: x = 1 + 1/x -> keep re-plugging the right-hand side into the x
on the RHS:

x = 1 + 1/(1 + 1/(1 + 1/...

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pklausler
Isn't the golden ratio x = 1/(x-1) ?

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pklausler
Never mind, they both work out to the same value.

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bogomipz
Its great to see Ramunujan getting a fair bit of attention these days. His
story is really fascinating. I can recommend:

[https://www.amazon.com/Man-Who-Knew-Infinity-
Ramanujan/dp/06...](https://www.amazon.com/Man-Who-Knew-Infinity-
Ramanujan/dp/0671750615)

This was also made into a movie a couple of months ago, I haven't seen the
movie but it should be on netflix/itunes by now since I don't think it had a
wide theatrical release.

[http://www.imdb.com/title/tt0787524/](http://www.imdb.com/title/tt0787524/)

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madcaptenor
Netflix currently says they're getting it in August 2016 (DVD; I don't know
about streaming)

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quantumhobbit
The house is #204 out of 288 houses. Assuming the house itself isn't counted
in either sum, which wasn't too clear by the question.

I got this by the definition of triangle numbers and solving n^2 = m(m+1)/2
for integer solutions. n is the house and m is the total of all houses. As
usual, I have no idea how Ramanujan did this with cont. fractions.

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rhizome
Thanks for the spoiler.

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quantumhobbit
Sorry about that. It isn't the full answer though.

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javajosh

       The sum of 1..n is n(n+1)/2. A.
       The sum of 1..N is N(N+1)/2. B.
       The sum of n..N = B-A.
       We want solutions to A = B-A. Or, 1 = B-A/A
    

I leave the rest as an exercise for the reader. :)

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spraak
I really enjoy Quanta Magazine's artwork featured on the articles!

