There has been a quite a bit of discussion on this forum regarding what Roger Penrose is asking for in this exercise. See:

http://www.roadtoreality.info/viewtopic.php?f=4&t=215
and
http://www.roadtoreality.info/viewtopic.php?f=19&t=276

In my attached solution I have stated at the beginning what I think Penrose is asking for. If anyone finds any errors or would like any clarifications, please contact me via this forum.
Vasco