Shipper's Dilemma Puzzle

Shipper's Dilemma Puzzle

John Conway devised this tricky puzzle.
Can you fit all 17 blocks into a cube?

(be careful the image of the photograph attached is staged, not a valid solution) 

This is a more advanced version of another puzzle:
 Puzzle - 24 Into 27 Will Go! by James Bromby | Download free STL model | Printables.com

There are five unit cubes, then there are six each of two other cuboids; 2x2x3 and 1x2x4. Your task is to assemble them into a 5x5x5 cube.

5 x Small Pieces of 1 x 1 x 1

6 x Medium Pieces of 2 x 2 x 3

6 x Large Pieces of 1 x 2 x 4

5 x (1 x 1 x 1) + 6 x (2 x 2 x 3) + 6 x (1 x 2 x 4) = 125

This equals five cubed, or 5 x 5 x 5 = 125

What to print:

One of each shape:

5 x Shippers Dilemma - Small Block.stl

6 x Shippers Dilemma - Medium Block.stl

6 x Shippers Dilemma - Large Block.stl

Optional: - Shippers Dilemma - 5x5 Board.stl

The models do not need supports and can be printed with standard settings. Advanced printers may want to iron the top surface to create a smooth look to the puzzle pieces.

Use multiple colours so that they can be distinguished or use a single colour for even more of a challenge (and print in one go, if your printer is large enough).

For compatibility with all of my other models, print a 100% scale.  If you scale any model, please remember the scaling factor and apply it to all models if you'd like them to be compatible.

How To Play:

Rotate and stack the pieces to form a 5x5x5 cube.