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## 'Mesh' printed from http://nrich.maths.org/

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A wire frame is made by wrapping a wire around the 'equator' of
a perfectly spherical balloon of unit radius and wrapping two wires
at right angles around the sphere going through the North and South
poles. The balloon is then deflated but remains perfectly spherical
until it can just be moved out of the framework. What is the radius
of the largest sphere that can pass through this frame, without
distorting it, from inside to outside?