Conjecturing and generalising

problem
Favourite

Negative Powers

Age

14 to 18

Challenge level

2 out of 3

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

1 out of 3

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

2 out of 3

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

1 out of 3

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

1 out of 3

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

Chocolate 2010

Age

14 to 16

Challenge level

1 out of 3

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

1 out of 3

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

1 out of 3

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

Simple Train Journeys

Age

5 to 11

Challenge level

1 out of 3

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
problem

Nim

Age

14 to 16

Challenge level

2 out of 3

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.