Inspirations from Easter Conferences - September 2006, All Stages

Problems

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Sort the Street

Stage: 1 Challenge Level: Challenge Level:1

Sort the houses in my street into different groups. Can you do it in any other ways?

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Numbers as Shapes

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

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Move a Match

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

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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Sticks and Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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Fraction Fascination

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

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Couples

Stage: 3 Challenge Level: Challenge Level:1

In a certain community two thirds of the adult men are married to three quarters of the adult women. How many adults would there be in the smallest community of this type?

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Magic Potting Sheds

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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More Magic Potting Sheds

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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Take Ten Sticks

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

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

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Odd Stones

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

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

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There's Always One Isn't There

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

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

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Number Chains

Stage: 5 Challenge Level: Challenge Level:1

Find all the periodic cycles and fixed points in this number sequence using any whole number as a starting point.

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Spirostars

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

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

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Spiroflowers

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.