Sets and Groups - March 2005, Stage 2&3

Problems

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Sorting Symmetries

Stage: 2 Challenge Level: Challenge Level:1

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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Butterfly Cards

Stage: 2 Challenge Level: Challenge Level:1

Four children were sharing a set of twenty-four butterfly cards. Are there any cards they all want? Are there any that none of them want?

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Sets of Four Numbers

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

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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Consecutive Seven

Stage: 3 Challenge Level: Challenge Level:1

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

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Arithmagons

Stage: 3 Challenge Level: Challenge Level:1

Can you find the values at the vertices when you know the values on the edges?

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Shuffle Shriek

Stage: 3 Challenge Level: Challenge Level:1

Can you find all the 4-ball shuffles?

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Stars

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?