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Radioactive material

A circle divided into six congruent sectors. A smaller concentric circle of radius one quarter of the large one. What fraction is black?

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Solution

The black fraction is 17/32.

Solution by Galip.

This solution uses the fact that the small sectors are 1/16 of the large ones. Because of rotational symmetry, only one third of the diagram needs to be examined.

Poem

Radioactivity
Makes love with
The lovely becquerels
Giving generously doses of rays
Silent and invisible enemy
Leading to a full catastrophy
No more romance in Fukushima
No more dance in Hiroshima
Only free and warm Xrays
People dying and fading away

Bella

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