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Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?

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Can you explain the strategy for winning this game with any target?

Tilted Squares

Age 11 to 14 Challenge Level:

We received three excellent solutions from Jonathan, Bryn and Marissa of Madras College. Marissa's solution follows:

The results above suggested a relationship between the area of tilted squares and the distance travelled along and up to get from one vertex to an adjacent vertex.
Alex from Llandovery College was able to prove the relationship and sent us this proof that the formula will always work.