Inky Cube

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

 
 
Image
Inky Cube
 
Here is a cube with nine small square patches on each of the six faces.
Some of the patches on each face are covered in ink.
All the faces are different.
 
The cube is placed on paper and makes a mark like this;
Image
Inky Cube
 

It is rolled over by tipping it very carefully (with no sliding) along one of the edges so that the next inky mark is right by its side. This gives;

Image
Inky Cube

It can roll both left and right and up and down.

When it has done several rolls, without taking it off, the paper looks like this;

Image
Inky Cube

Your challenge is to find out:

  • where the inky spots are on each of the six faces
  • where the cube was first placed
  • the route that the cube has taken.
All the faces might not have been used for this example.
 
Here is a printable version of the marks left by the cube. 
 
--------------------
 

Next, you might like to try this colour version where you have to find the colours for each patch on each of the faces of the cube, as well as the route it took.

 
Image
Inky Cube
 

Here is a printable version of the marks left by this coloured cube.