Congratulations to this week's winner

Steven Noto

Correct solutions were also received from Ray Kremer, Mike Fitzpatrick, and Yan Fridman.

Steven's solution was by far the most simple and elegant, using nothing but simple geometry. Refer to the diagram for the definitions of the variables r, y, z. From the diagram of the problem one immediately sees that

y + z = 1
2r + z = y
(r + z)² + (3r + z)² = 1

The three equations in the three unknown are easy to solve and give the answer of

r =

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