Problems
Star Find
Stage: 1 Challenge Level: 
Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?
Four Colours
Stage: 1 Challenge Level:
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Jigsaw Pieces
Stage: 1 Challenge Level:
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
Tessellating Triangles
Stage: 2 Challenge Level:
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
Two by One
Stage: 2 Challenge Level:
An activity making various patterns with 2 x 1 rectangular tiles.
World of Tan - Pentominoes
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outlines of these people?
Tetrafit
Stage: 2 Challenge Level:
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Rod Measures
Stage: 2 Challenge Level:
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
Islamic Tiling
Stage: 3 Challenge Level:
One rich source of tilings is to found in the mausoleums, mosques and minarets found throughout the Islamic world. Below are three particular favourites of mine. Study them carefully, locate the. . . .
Cogs
Stage: 3 Challenge Level:
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Marvellous Matrix
Stage: 3 Challenge Level:
Circle any number in the matrix, for example, 608 as below. Draw a line through all the squares that lie in the same row and column as your selected number. Circle another number which has not got. . . .
Eminit
Stage: 3 Challenge Level:
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
Sixational
Stage: 4 Challenge Level:
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
Get Cross
Stage: 4 Challenge Level:
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
Matter of Scale
Stage: 4 Challenge Level:
Prove Pythagoras Theorem using enlargements and scale factors.
Big, Bigger, Biggest
Stage: 5 Challenge Level:
Which is the biggest and which the smallest of these numbers and by how do they compare in magnitude? A = 2000^{2002} B = 2001^{2001} C = 2002^{2000}
Proof Sorter - Sum of an AP
Stage: 5 Challenge Level:
Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing
