Problems
Christmas Shopping
Stage: 2 Challenge Level: 
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
More Christmas Boxes
Stage: 2 Challenge Level:
What size square should you cut out of each corner of a 10 x 10 grid to make the box that would hold the greatest number of cubes?
Train Carriages
Stage: 2 Challenge Level:
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
World of Tan - Mai Ling
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Mai Ling?
Sam Again
Stage: 3 Challenge Level:
Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.
Christmas Boxes
Stage: 3 Challenge Level:
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
As Easy as 1,2,3
Stage: 3 Challenge Level:
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
Farmers Field
Stage: 3 Challenge Level:
A farmer has a flat field and two sons who will each inherit half of the field. The farmer wishes to build a stone wall to divide the field in two so each son inherits the same area. Stone walls are. . . .
Rolling Triangle
Stage: 3 Challenge Level:
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
Special Sums and Products
Stage: 3 Challenge Level:
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
LOGO Challenge 10 - Circles
Stage: 3 and 4 Challenge Level:
In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.
Wrapping Gifts
Stage: 4 Challenge Level:
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be? Now suppose we want to wrap up a. . . .
Doodles
Stage: 4 Challenge Level:
A 'doodle' is a closed intersecting curve drawn without taking pencil from paper. Only two lines cross at each intersection or vertex (never 3), that is the vertex points must be 'double points' not. . . .
Holly
Stage: 4 Challenge Level:
The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.
Giant Holly Leaf
Stage: 4 Challenge Level:
Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).
Elsewhere...
Featured Solutions
Articles & Games
Learning Mathematics Through Games Series: 2.types of Games
This article, the second in the series, looks at some different types of games and the sort of mathematical thinking they can develop.
