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The sneak peek

A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?

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Intermediate

Take five origami

Divide a rectangular piece of paper in five pieces of equal area. You only have a pair of scissors at your disposal, but you are allowed to make straight folds to guide you.

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Intermediate

The kingsize bed

A rectangle with an inscribed right triangle. What is ac/bd?

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Intermediate

The folded napkin

A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?

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Beginner

The bobline

A regular hexagon is folded back and forth along the dotted line. What fraction of the area is yellow?

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Intermediate

The folded triangle

An equilateral triangle is folded with its left side at right angles with the base. What fraction of the total triangle is shaded?

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Beginner

The folded sheet

A rectangular sheet of paper is folded in such a way that two equal angles are formed as shown. What fraction of the resulting quadrilateral is shaded?