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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Can you fit the tangram pieces into the outline of Mai Ling?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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?
What is the sum of all the three digit whole numbers?
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. . . .
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. . . .
Find all the ways to cut out a 'net' of six squares that can be
folded into a cube.
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.
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.
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.
In LOGO circles can be described in terms of polygons with an
infinite (in this case large number) of sides - investigate this
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. . . .
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.
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).
What if the Earth's shape was a cube or a cone or a pyramid or a
saddle ... See some curious worlds here.
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?
This article, the second in the series, looks at some different types of games and the sort of mathematical thinking they can develop.