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Intermediate

The arena

In a circular arena two contestants are leaving from points A and B. Their respective speeds are such that they would collide at point C, but just before they do they exchange directions. Then they hit the edge of the arena and return to their starting points. During the whole race, A and B move […]

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Advanced

The rolling stones

If you roll a circle down a parabola, small circles can roll all the way down and up, whereas large circles get stuck between the sides at some point. What is the transition radius? In other words, what’s the maximum circle that keeps on rolling?

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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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Intermediate

The ricochet

An isosceles triangle with base 10 and sides 13. What is the total length of the red line segments?

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Intermediate

Triangular billiards

A ball track starts halfway the left side of an equilateral triangular billiard table having side length 2. After two bounces it arrives in the top corner. What’s the total track length?

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Intermediate

The pulley problem

Two pulleys carrying three weights of 30, 70 and 50 grams. Given that the constellation is in equilibrium, what’s the angle?

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Intermediate

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?

Categories
Intermediate

The corner pocket

A snooker player wants to corner a ball starting from a point on one side and bouncing two times from the opposite sides. Given the dimensions of the table in the figure, what’s the length of the track the snooker ball travels?