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The ocean sunset

A semicircle is inscribed in a rectangle. What is the minimal covered fraction?

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The lemon slice

A semicircle is inscribed in a quarter circle. What is the minimal yellow fraction?

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The Common Snowdrop

A square contains a smaller square. Their vertices are cyclically connected as shown, forming four triangles. What is the minimal green area fraction?

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Intermediate

The magic mirror

You are standing in front of a mirror. Your shoulder width is 50 cm and your eyes are 6 cm apart. What is the minimum mirror width for a stereo view of yourself?

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Who’s afraid of red, yellow and blue?

Three squares. The top line segment is variable in length. What’s the minimal blue fraction?

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The party hat

A cone has height 6 and base diameter 6. On it lie two points, one exactly halfway up, the other diametrically opposed at the base. What’s the shortest distance between these points going along the cone surface?

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The lazy spider

A spider situated at point A on the outside of a cylinder with diameter 4 and height 3 is trying to get to a fly at point C on the complete opposite side as fast as possible. What is the shortest route?