Jane Street June ’20 (Circle Time)

The problem, found here: https://www.janestreet.com/puzzles/circle-time/
The problem, stolen directly from https://www.janestreet.com/puzzles/circle-time/
The red circle C containing a “ring” of green circles
Area of the green ring of circles
Area of the circle C
The proportion of area with a single ring of circles
The sum of the geometric series of the rings of circles
The geometric series of λ² can be seen with a coefficient
The sum of a convergent geometric series
The sum of all rings of circles
Notice that we’ve replaced the infinite series part with a closed-form formula
The final proportion depends solely on the ratio between radii of the circles of rings
Both blue and red circles depend solely on the chosen k
Our very educated guess is supported by animation!
Our awesome system of equations that will let us solve for k
x and y coordinates that we can now use
yikes…I don’t want to solve this… Oh, wait… I’m writing the article…

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Dhrumil Patel

Dhrumil Patel

Hey! I'm excited about deep learning, cybersecurity and neurotechnology.