Conjecturing and generalising

problem
Favourite

Negative Powers

Age

14 to 18

Challenge level

What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?
problem
Favourite

Tangled Trig Graphs

Age

16 to 18

Challenge level

Can you work out the equations of the trig graphs I used to make my pattern?
problem
Favourite

Shape and Territory

Age

16 to 18

Challenge level

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
problem

Absurdity Again

Age

16 to 18

Challenge level

What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?
problem

Incircles

Age

16 to 18

Challenge level

The incircles of 3, 4, 5 and of 5, 12, 13 right angled triangles have radii 1 and 2 units respectively. What about triangles with an inradius of 3, 4 or 5 or ...?
problem

Threesomes

Age

11 to 14

Challenge level

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?
problem

Chocolate 2010

Age

14 to 16

Challenge level

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...
problem

Taking Steps

Age

7 to 11

Challenge level

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
problem

Squares, Squares and More Squares

Age

11 to 14

Challenge level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
problem

Dotty Triangles

Age

11 to 14

Challenge level

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?