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Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

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Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

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Maximum Flow

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

Mach Attack

Stage: 5 Challenge Level: Challenge Level:1

This problem is aimed at interested and enthusiastic students: although we don't recommend it for mainstream classroom use it provides enrichment and will develop mathematical thinking and knowledge.

Like all NRICH problems it has been carefully designed to be full of mathematical interest and as such might be used in a variety of ways: you might suggest that keen students consider the problem in their own time, use it for a maths club at school or use it in class as a vehicle to foster discussion and mathematical thinking. See our Teachers Guide to Getting Started with rich tasks for more suggestions and ideas.
This problem will be of particular interest to students considering a university course containing an element of mathematical physics.