3D Shapes - Short Problems

Red or Black

Stage: 3 and 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?

Cubic Covering

Stage: 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?

Blockupied

Stage: 3 and 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?

Extended Cube

Stage: 3 and 4 Short Challenge Level:

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

Stage: 3 and 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?

Twelve Cubed

Stage: 3 and 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

Stage: 3 and 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?

Sugary Diversion

Stage: 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

Stage: 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

Stage: 3 Short Challenge Level:

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

Painted Purple

Stage: 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

Stage: 3 Short Challenge Level:

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

Crawl Around the Cube

Stage: 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?

Facial Sums

Stage: 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?

Truncated Tetrahedron

Stage: 3 and 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?

Painted Octahedron

Stage: 3 and 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?

Pyramidal N-gon

Stage: 3 and 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?