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Threesomes

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?

Mind Reading

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?

Have You Got It?

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

2001 Spatial Oddity

Age 11 to 14 Challenge Level:

16cm x 9cm sqaure, cut, then made into 12cm x 12cm square.

A 16 cm by 9 cm piece of card can be cut into two pieces which can be rearranged to form a 12 cm by 12 cm square. Explain how this can be done.

Find the dimensions of other rectangles that can be cut into exactly two pieces and rearranged to form a square.