A schematic of the solution is shown
below. The information from the
question is given in black. Deductions directly from this information
are
given in red. Points that provide potential key information are shown
by
green arrows which leads to the structures which are linked via the
blue
arrows to show the path required to work them all out. The "key
information"
that allows the correct solution to be found is that **F** is an
alkene
with only 2 types of C, this gives **E** and then **D **from
which
the others are deduced. **D** reacts with HBr via SN1 reaction
hence
the rearrangement.

There are, of course, other possible thought pathways.