Farewell to Jenny Piggott - January 2011, Stage 4&5

In the summer of 2010, Jenny Piggott retired as NRICH Director and we held a farewell event for her. Colleagues and friends joined us to work together on problems they had suggested. This month we are featuring some tasks that were inspired by the day.

Problems

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Odds and Evens

Stage: 3 and 4 Challenge Level: Challenge Level:1

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

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Which Solids Can We Make?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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Fit for Photocopying

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Photocopiers can reduce from A3 to A4 without distorting the image. Explore the relationships between different paper sizes that make this possible.

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Difference Dynamics

Stage: 4 and 5 Challenge Level: Challenge Level:1

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

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Dicey Decisions

Stage: 5 Challenge Level: Challenge Level:1

Can you devise a fair scoring system when dice land edge-up or corner-up?

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Weekly Challenge 16: Archimedes Numerical Roots

Stage: 5 Challenge Level: Challenge Level:1

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

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Ante Up

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Use cunning to work out a strategy to win this game.