problem
Favourite
Tet-trouble
Age
14 to 16
Challenge level
Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?
problem
Favourite
Nine colours
Age
11 to 16
Challenge level
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
Favourite
Marbles in a box
Age
11 to 16
Challenge level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Favourite
Triangles to tetrahedra
Age
11 to 14
Challenge level
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
problem
Red or black
Age
11 to 14
Challenge level
How many edges of a cube need to be coloured black to mean every face has at least one black edge?
problem
Cubic covering
Age
14 to 16
Challenge level
A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?
problem
Blockupied
Age
11 to 14
Challenge level
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?
problem
Daniel's star
Age
11 to 14
Challenge level
A solid 'star' shape is created. How many faces does it have?
problem
Twelve cubed
Age
14 to 16
Challenge level
A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?
problem
Dicey directions
Age
14 to 16
Challenge level
An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?
problem
Net result
Age
11 to 14
Challenge level
The net shown here is cut out and folded to form a cube. Which face is then opposite the face marked X?
problem
Painted purple
Age
14 to 16
Challenge level
Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?
problem
Magic octahedron
Age
11 to 14
Challenge level
Weekly Problem 20 - 2010
You have already used Magic Squares, now meet a Magic Octahedron...
You have already used Magic Squares, now meet a Magic Octahedron...
problem
Crawl around the cube
Age
11 to 14
Challenge level
Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?
problem
Facial sums
Age
14 to 16
Challenge level
Can you make the numbers around each face of this solid add up to the same total?
problem
Truncated tetrahedron
Age
11 to 14
Challenge level
A tetrahedron has each corner cut off to produce a solid. What is the total length of the edges of this solid?
problem
Painted octahedron
Age
11 to 14
Challenge level
What is the smallest number of colours needed to paint the faces of a regular octahedron so that no adjacent faces are the same colour?
problem
Pyramidal n-gon
Age
14 to 16
Challenge level
The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?
problem
Net profit
Age
11 to 14
Challenge level
The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube?
problem
Four cubes
Age
14 to 16
Challenge level
Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?
problem
Same face
Age
11 to 14
Challenge level
A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?
problem
Stretched surfaces
Age
14 to 16
Challenge level
The edges of a cube are stretched, can you find the new surface area?
problem
Rotation identification
Age
11 to 14
Challenge level
Which of these can be obtained by rotating this shape?
problem
Which face?
Age
14 to 16
Challenge level
Which faces are opposite each other when this net is folded into a cube?
problem
Multiplication cube
Age
11 to 14
Challenge level
The net shown is folded up to form a cube. What is the largest possible vertex product?