Current Puzzle

Circle Time

Call a “ring” of circles a collection of six circles of equal radius, say r, whose centers lie on the six vertices of a regular hexagon with side length 2r. This makes each circle tangent to its two neighbors, and we can call the center of the regular hexagon the “center” of the ring of circles. If we are given a circle C, what is the maximum proportion of the area of that circle we can cover with rings of circles entirely contained within C that all are mutually disjoint and share the same center?

When submitting an answer, you can either send in a closed-form solution, or your answer out to 6 decimal places.

Correct Submissions as of 04/06/20

Zihao Li
Rahul Saxena
Guillermo Wildschut
Will Gulian
Michal Mráz
Cubist
Kristof S
Pavle Vuksanovic
Richard Li
Kevin Li
calum
Neil Thistlethwaite
Glauber Guarinello
Rodrigo Amorim
Edgar Wang
Magister Mugit
Mihail Tarigradschi
sniffleheim
Arkya Chatterjee
sal gabbordo
Alex Kalbach
Gordon Macshane
Siyu Chen
googlweknoall
Andrew T.
Jeffrey Fu
Sean Egan
Sanandan Sandman
Konstantin Vladimirov
Kyle Craig
Andrew Tran
Sergey Tychinin
Jack Dylan
Sunny Lee
Cory Nezin
Abhinav Mukherjee
Guillaume C.
NMS
Wula
Dimas Ramos
Keith Schneider
Hudson Vieira
costica147
Mykyta Makovenko
Ezio
Will Liao
Kristijan Stefanec
zhelih
cssachse
Alvin Chiu
Angus King
TimDong
Benjamin Frady & Ohad Rau
Garrett Andersen
Jesse Y.
Cooper Young
Heidi Stockton
MP
Arne Schneuing
Daniel Lin
Matt Johnson
Felix Berief
maiii
Michael DeLyser
sophy
SeeSoftware
Haotian Wang
Erik-Cristian Seulean
Max Jackson
Mikhail Soumar
Tadek Krassowski
Glenn Dixon
PB
Danil Savine



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