If you haven’t seen Matt Parker’s Christmas Tree folding puzzle or received in on email/mail yet, you can read about it in one of his recent videos: I can confirm that it does fold in to a few different shapes!
The full “tree” is cut out including brown and yellow. One way that you can consider what is possible for the given paper shape, is to count the boxes. The boxes needed for each shape will be x*2*y*2*x*y*2 for each x by y by 1 box.
This may be easy enough to calculate for 1x1x1, which is 6 faces, but how about finding all the ways this specific net can be folded? A spreadsheet as usual comes in handy: Remember that “$” locks in the row or column, for example “$B4” would be always B even when dragged to fill right and down with the bottom right corner. Dragging the formula to the right and down will bring you something like this:
With the net that Matt Parker sent out, there are 22 squares. What can it possibly turn in to according to the above chart? a 2×3 or a 5×1 (or equivalently, 3x2x1 or 1x5x1 cubic).
(Spoilers below if you want to see how it is assembled – it does indeed fold to a 1×5 or a 3×2… and an “L” shape 🙂
