This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
A task which depends on members of the group working collaboratively to reach a single goal.
