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Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Junior Frogs

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Three Sets of Cubes, Two Surfaces

How many models can you find which obey these rules?

Inky Cube

Age 7 to 14
Challenge Level
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;
 3 spots

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;

 2 places

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;


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.


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