Age 7 to 16
Students could be challenged to visualise how the different cubes could be constructed from the net.
Perhaps working in pairs, students could try to convince each other why (and how) certain cubes can be made, and why certain cubes cannot be made.
Copies of the printed sheets, scissors and sticky tape could be made available at a later stage to allow students to cut up the net and make the various cubes to check their predictions.
The second part of the problem could be tackled in a similar way.