Candy Corn Concentric Circles II

Geometry Level 2

As shown below, the diagram consists of four concentric circles and the positive-integer-valued widths z 1 , z 2 , z 3 , z 4 z_1, z_2, z_3, z_4 . Both yellow and orange regions have the same combined areas, which exist for z 1 = z 2 = z 3 = z 4 z_1 = z_2 = z_3 = z_4 .

But is it possible for z 1 > z 4 z_1 > z_4 ?

No. Yes.

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1 solution

Victor Chan
Jan 18, 2021

Andrew Hayes' solution to part 1 has z 1 > z 4 z_1 > z_4 :

( z 1 , z 2 , z 3 , z 4 ) = ( 7 , 1 , 3 , 1 ) (z_1, z_2, z_3, z_4) = (7, 1, 3, 1) .

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