CAD Challenge finished with Solvespace after watching Paul Randall's attempt on his YouTube channel. Paul asked me to make a video of it so here it is. Completing the challenge is absolutely possible with Solvespace.
The original challenge can be found here: http://computeraideddesignguide.com/wp-content/uploads/2014/04/autocad3d27.png
If you want to see Paul complete the challenge with FreeCAD. Here is a link to his video: https://www.youtube.com/watch?v=r1x5kku10-k&t=713s
If you want to download my file you can find it here: https://my.hidrive.com/lnk/QkI4MFhQu
For this challenge I used Solvespace 2.3 on OSX.
Solvespace is open source (GPLv3 license) and is available for Window, OSX and Linux. It is developed by Jonathan Westhues and maintained by Whitequark and others. It can be downloaded here: http://solvespace.com/download.pl