3x3x3
At the London Hackspace they have a cube which posses an interesting tessellation problem. The aim of the puzzle is to make a perfect cube from the individual static shapes. There is apparently only one solution to the problem of making a perfect cube from the component parts.
In trying to solve the problem I chanced upon a new conundrum I began to try to make the complete cube with only 1 block difference outside of the perfect cube. I managed 3 variations in one session, two were repetitions of each other before my hands started to hurt and I began to think through the alternative puzzle
I will add a picture of one of the one block solutions to give you an idea of the puzzle. The first two were differences on the same plane and the second on an alternate side.
After considering the puzzle and some reminders to think through the simpler alternative one block difference solutions I came to the conclusion that there are around 9 one block differences to that particular puzzle excluding variations.