Problems
Colouring Triangles
Stage: 1 Challenge Level: 
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
Knight's Swap
Stage: 2 Challenge Level:
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Midpoint Triangle
Stage: 2 Challenge Level:
Can you cut up a square in the way shown and make the pieces into a triangle?
A Rod and a Pole
Stage: 2 Challenge Level:
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
World of Tan - Gat Marn
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of this plaque design?
Book Codes
Stage: 2 Challenge Level:
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Ice Cream
Stage: 2 Challenge Level:
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Pick
Stage: 3 Challenge Level:
Investigate polygons with all the vertices on the lattice points of a grid. For each polygon, work out the area A, the number B of points on the boundary and the number of points (I) inside. . . .
Good Work If You Can Get It
Stage: 3 Challenge Level:
A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?
Read This Page
Stage: 3 Challenge Level:
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Days and Dates
Stage: 4 Challenge Level:
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
The Medieval Octagon
Stage: 4 Challenge Level:
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Never Prime
Stage: 4 Challenge Level:
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
LOGO Challenge - Pentagram Pylons
Stage: 3, 4 and 5 Challenge Level:
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
Shape and Territory
Stage: 5 Challenge Level:
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
Napoleon's Hat
Stage: 5 Challenge Level:
Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?
Elsewhere...
Featured Solutions
Articles & Games
Learning Mathematics Through Games Series: 4. from Strategy Games
Basic strategy games are particularly suitable as starting points for investigations. Players instinctively try to discover a winning strategy, and usually the best way to do this is to analyse the outcomes of series of 'moves'. With a little encouragement from the teacher, a mathematical investigation is born.
