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Hex

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

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Triangular Tantaliser

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

Overlap

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

A red square and a blue square of side $s$ are overlapping so that the corner of the red square rests on the centre of the blue square.

Show that, whatever the orientation of the red square, it covers a quarter of the blue square.

If the red square is smaller than the blue square what is the smallest length its side can have for your proof to remain true?

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