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## The askew envelope

In a square, an interior point is drawn with an angle to the top vertices of 120°. What’s the angle between the chords formed by the two arcs centered in these vertices?

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## The fishing net

Two squares and two equilateral triangles. What fraction is hatched?

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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?

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## The inner wheel

A wheel is placed inside another that has exactly twice its radius. If the inner wheel rolls around once without slipping, how many revolutions has it completed?

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## The broken window

A square is divided into triangles and quadrilaterals as shown. What fraction of the square area is covered by the shaded triangle?

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## The shark fin

An isosceles triangle is inscribed in a semicircle with one side along the diagonal and the top vertex somewhere on the semicircle. What’s the maximum fraction shaded?

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## The diagonal dilemma

On two faces of a cube a diagonal is drawn that meet in the same vertex. What’s the angle between them?

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## The blockhat

Four congruent rectangles are placed in a hat-shaped configuration. What’s the angle between the lines connecting the opposite corners?

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