Shape - May 2006, All Stages

Problems

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Tessellate the Triominoes

Age 5 to 7 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

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Cover the Camel

Age 5 to 7 Challenge Level:

Can you cover the camel with these pieces?

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Triangle Animals

Age 5 to 7 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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Tangram Tangle

Age 5 to 7 Challenge Level:

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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A Patchwork Piece

Age 7 to 11 Challenge Level:

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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Seven Flipped

Age 7 to 11 Challenge Level:

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Semi-regular Tessellations

Age 11 to 14 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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Concrete Wheel

Age 11 to 14 Challenge Level:

A huge wheel is rolling past your window. What do you see?

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Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate?

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A Roll of Patterned Paper

Age 14 to 16 Challenge Level:

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

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One Reflection Implies Another

Age 14 to 16 Challenge Level:

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .

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Rotations Are Not Single Round Here

Age 14 to 16 Challenge Level:

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .

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Spokes

Age 16 to 18 Challenge Level:

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

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Footprints

Age 16 to 18 Challenge Level:

Make a footprint pattern using only reflections.

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Gold Yet Again

Age 16 to 18 Challenge Level:

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."