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Advanced

The maxbox

A square containing a red square of variable size sharing a vertex with a blue rectangle. What is the maximal blue fraction?

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Intermediate

The motorcycle

Two congruent orange circles and a smaller blue one. Three common tangents are shown, one of which passes through a circle centre. What is the proportion blue : orange?

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Intermediate

Sharing is caring

Three equilateral triangles and three shared vertices. What’s the proportion blue : green?

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Beginner

The fried egg

Two concentric circles and two tangents. What is the yellow fraction?

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Intermediate

The piercing

An equilateral triangle containing a right triangle and a line segment. What fraction is pink?

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Intermediate

The crazy quilt

A parallelogram is divided into several areas. What is the area X of the blue trapezium?

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Advanced

The bell tolls

An equilateral triangle inscribed in a rectangle. What is its area X in terms of triangle areas A and B?

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Intermediate

The Pisa experiment

Four squares and an altitude to the top vertex form a right yellow traingle. What is the proportion yellow : green?

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Beginner

The parrot

Two squares, a diagonal and a line segment. What is red : blue : green?

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Intermediate

Boxed in

A square with an inscribed right triangle. What fraction is yellow?