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You are given a limitless supply of triangular jigsaw pieces of type T1, T2, T3, T4 and T5
Using these pieces, you need to try to make larger triangular shapes without any overlap.
Three triangle shapes are shown in the picture below. Is it possible to create two-coloured triangles of these shapes without moving the pieces already placed?
Suppose next that you can move the pieces and choose two triangle types to work with. Which pairs of shapes can be used to make larger equilateral triangles? Which pairs of shapes can be used to make larger 30-60-90 triangles? See the video clip for a discussion on this part of the problem
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?