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Favourite
Tet-Trouble
Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?
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Favourite
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?
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Favourite
Marbles in a box
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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Favourite
Triangles to Tetrahedra
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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Red or Black
How many edges of a cube need to be coloured black to mean every face has at least one black edge?
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Cubic Covering
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?
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Blockupied
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?
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Twelve Cubed
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?
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Dicey Directions
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?
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Net Result
The net shown here is cut out and folded to form a cube. Which face is then opposite the face marked X?
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Painted Purple
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?
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Magic Octahedron
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...
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Crawl Around the Cube
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?
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Facial Sums
Can you make the numbers around each face of this solid add up to the same total?
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Truncated Tetrahedron
A tetrahedron has each corner cut off to produce a solid. What is the total length of the edges of this solid?
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Painted Octahedron
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?
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Pyramidal n-gon
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?
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Net Profit
The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube?
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Four Cubes
Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?
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Same Face
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?
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Multiplication Cube
The net shown is folded up to form a cube. What is the largest possible vertex product?