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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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Beginner

The glass ceiling

Three squares, two of which share a vertex. What is the total area?

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Beginner

Three folds

A square divided by three line segments. What’s the proportion yellow : purple?

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Intermediate

Égalité

A square with its diagonal and a circle. If red is equal to blue, what’s the angle α?

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Spiegel im Spiegel

A triangle with an inscribed triangle. What fraction of the former does the latter cover in terms of lengths a, b, c, d, e and f?

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Beginner

The green necktie

A square with several line segments. What fraction is green?

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Intermediate

House of Orange

A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?

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Out of proportion

An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?

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Intermediate

Head above water

A unit square with an extended side immersed in another square. What is the area of the red triangle?

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Intermediate

The framing effect

Four squares, three of which are coloured. What’s the area of the blue one?