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'3 Sets of Cubes, 2 Surfaces' printed from http://nrich.maths.org/

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This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)
It can be used as a follow-on from Two on Five.
 
You have interlocking cubes of three different colours - $2$ of one colour, $3$ of another colour and $4$ of the third colour.
It could look like this;
2,3,4

 This is slightly different from Two on Five but is seen as an extension for the highest attaining. You might like to go there first!
 
The nine cubes are to be connected in the usual way with the following rules being applied.
 
THE TWO YELLOW CUBES ARE NOT ALLOWED TO TOUCH WALL OR FLOOR SURFACES.
 
THE THREE BLUE CUBES MUST TOUCH ONE SURFACE ONLY, NOT TWO.
 
THE FOUR RED CUBES MUST TOUCH BOTH SURFACES.
 
Here are two examples that obey the rules;
 

 new 2on3on4
 
See what others you can find.
How many will there be?
At some point ask yourself "I wonder what would happen if I ...?"