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Age 16 to 18
Challenge Level Yellow star
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You want to get across a square ploughed field from one corner to the opposite corner as quickly as possible. There is a path along one edge of the field but the rest of the field is ploughed right up to the other three edges. On the ploughed land you can walk at 6 km per hour. From where you are standing you can walk on the path along one edge of the field at 10 km per hour, but there are no paths along the other edges of the field. What is the best route to take?
Suppose the edge of the field is one kilometre in length. What is the shortest time in which you can cross the field to the opposite corner?

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Generally Geometric

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.

Bend

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

Exponential Trend

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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