Just completed it I did not cheat, it took I while I must admit but as it does say 'around' the key to solving it is becoming familiar with the pieces - experience of the shapes and the slotting is the answer.
I found that if I was one 'unit' off it all fitting in I would think wow thats close and will spend ages just moving a few at the top round, the problem being I would get stuck in a rutt.
Changing your mind set and attempting different solutions such as slotting 2 pieces together out side the box into useful shapes and then slotting them in the box rather than one at the time.
I solved it by slotting it together on the inside of the lid and next to the box this allows you to keep to the right size while making it easier to piece together.
I started my solution with the x and the w shaped pieces at the very bottom togther and the more difficult shaped pieces slotted around them so to get them out of the way!!
Good luck.