Problems
Chain of Changes
Stage: 1 Challenge Level: 
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
The Lily Pond
Stage: 2 Challenge Level:
Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go?
A Cartesian Puzzle
Stage: 2 Challenge Level:
Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
Treasure Island
Stage: 2 Challenge Level:
Write down what you can see at the coordinates of the treasure island map. The words can be used in a special way to find the buried treasure. Can you work out where it is?
What Are You Plotting?
Stage: 2 Challenge Level:
Investigate the positions of points which have particular x and y coordinates. What do you notice?
Teddy Town
Stage: 1, 2 and 3 Challenge Level:
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Coordinate Tan
Stage: 2 Challenge Level:
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
World of Tan - Concentrating on Coordinates
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Red Even
Stage: 2 Challenge Level:
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
Transformation Tease
Stage: 2 Challenge Level:
What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?
Plate Spotting
Stage: 2 Challenge Level:
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
Going Loopy
Stage: 3 Challenge Level:
Spiralling out of control! I should have known better. Merely mentioning the word spiral and suggestions and reminders abound. Below are some spirals done by pupils at a recent Masterclass at the. . . .
Powerful Factorial
Stage: 3 Challenge Level:
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?
Domino Tetrads
Stage: 3 Challenge Level:
Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?
Similarly So
Stage: 4 Challenge Level:
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
Approximating Pi
Stage: 4 Challenge Level:
By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
30-60-90 Polypuzzle
Stage: 5 Challenge Level:
Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.
Double Angle Triples
Stage: 5 Challenge Level:
Consider the triangle ABC where angle B is twice angle A. Show b^2=a^2+ac. Find integer solutions of this equation.
Binary Squares
Stage: 5 Challenge Level:
If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?
Remainder Hunt
Stage: 5 Challenge Level:
What are the possible remainders when the 100-th power of an integer is divided by 125?
