2D representations of 3D shapes
problem
Can you find out which 3D shape your partner has chosen before they work out your shape?
problem
Nine colours
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
problem
Arranging cubes
A task which depends on members of the group working collaboratively to reach a single goal.
problem
The third dimension
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
problem
Which solids can we make?
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
problem
Building blocks
Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?
problem
The spider and the fly
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
problem
Hamiltonian cube
Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
Find the length along the shortest path passing through certain points on the cube.
problem
Picture a pyramid
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
problem
A city of towers
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?