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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?