I remember there was an episode in Outer Limits with a similar premise. Everyone's brain is wired to this enormous data source making traditional study obsolete except for one guy who for some medical reason can't accept the implants.

Dave, you are my hero.

then there is no computer program that can complete them quickly from scratch.

If you have that much gasoline to spear in the post-apocalyptic world I would aalso recommend an all-terrain carrier such as Bandvagn 206. They can swim and also work great in snow and extremely steep hills.