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Seven Sticks

Age 5 to 7
Challenge Level Yellow star
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Jordan, Harry, Stan and Julia from Dennington Primary School have been experimenting with this problem. All of them found this arrangement of the seven sticks:

triangle made of base 3 sticks and sides 2 sticks each

Harry, Stan and Julia found this:

2 identical triangles with sides of 1 stick pushed together so bases touch

Harry and Julia both managed to arrange the sticks to form these two sets of triangles:

an equilateral triangle of 3 sticks with two triangles off one of its sides using 2 more sticks each
2 equilateral triangles arranged corner to corner like arrow heads pointing towards each other, 7th stick laid to side forming new triangle

Stan was the only one to find this arrangement:

equilateral triangle made with 3 sticks then another equilateral triangle made with base of first so they point like arrow heads away from each other. Last two sticks make another triangle using part of one side as base

You have all been very imaginative - well done. I wonder whether you can find any others?


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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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