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Pinned Squares

The diagram shows a 5 by 5 geoboard with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins. What is the total number of squares that can be made on a 5 by 5 board?

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This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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Power Crazy

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?


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

If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation? Explain your reasoning. Draw some diagrams of your own and mark in these angles. If in addition you know that the lines $AB$ and $CD$ are parallel which angles can you find?