# 3D Shapes - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on 3D Shapes.

### Facial Sums

##### KS 3 Short Challenge Level:

Weekly Problem 41 - 2010
Can you make the numbers around each face of this solid add up to the same total?

### Sugary Diversion

##### KS 3 Short Challenge Level:

Weekly Problem 48 - 2008
An ant is crawling in a straight line when he bumps into a one centimetre cube of sugar.If he climbs over it before before continuing on his intended route, how much does the detour add to the length of his journey?

### Net Result

##### KS 3 Short Challenge Level:

Weekly Problem 5 - 2009
The net shown here is cut out and folded to form a cube. Which face is then opposite the face marked X?

### Cubic Vision

##### KS 3 Short Challenge Level:

Weekly Problem 1 - 2010
How many cubes can you see?

### Painted Purple

##### KS 3 Short Challenge Level:

Weekly Problem 18 - 2010
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?

### Magic Octahedron

##### KS 3 Short Challenge Level:

Weekly Problem 20 - 2010
You have already used Magic Squares, now meet a Magic Octahedron...

### Crawl Around the Cube

##### KS 3 Short 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?

### Cubic Covering

##### KS 3 Short Challenge Level:

Weekly Problem 31 - 2006
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?

### Red or Black

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 1 - 2012
How many edges of a cube need to be coloured black to mean every face has at least one black edge?

### Truncated Tetrahedron

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 2 - 2012
A tetrahedron has each corner cut off to produce a solid. What is the total length of the edges of this solid?

### Blockupied

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 28 - 2007
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

### Painted Octahedron

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 4 - 2014
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?

### Extended Cube

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 39 - 2007
A solid 'star' shape is created. How many faces does it have?

### Pyramidal N-gon

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 43 - 2014
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?

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 46 - 2007
When a solid cube is held up to the light, how many of the shapes shown could its shadow have?

### Net Profit

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 41 - 2015
The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube?

### Twelve Cubed

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 19 - 2008
A wooden cube with edge length 12cm is cut into cubes with edge length 1cm. What is the total length of the all the edges of these centimetre cubes?

### Dicey Directions

##### KS 3 & 4 Short Challenge Level:

Weekly Problem 25 - 2008
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?