= Solution
Use a four-state <Moore machine>. In state $A$ wait for an outer-sensor activation; $B$ combines the outer-only and both-sensors phases; $C$ records that the visitor has reached the inner-only phase; $I$ emits the one-cycle count pulse. Only $I$ has `INC = 1`.
The complete <state transition table>, with input order $x_1x_0$, is
``
state 00 01 11 10 INC
A A B B A 0
B A B B C 0
C I B B C 0
I A B B A 1
``
For a normal entry the states are $A\to B\to B\to C\to I$; retreat after the first sensor instead gives $A\to B\to A$ with no pulse. Repeated samples at one sensor remain in the corresponding phase. State $I$ always exits on the next edge, so its output lasts exactly one clock period; an outer activation on that next edge goes directly to $B$, allowing the next visitor to start immediately.
This follows the question's single-visitor entry model and merges the two outer-active phases as its hint requests. Inputs are sampled synchronously; the table also specifies deterministic recovery for other sampled combinations. It is not a specification of a bidirectional occupancy counter for arbitrary overlapping entry and exit traffic.
\Image[/past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/digital-resit-visitor-controller.png]
{title=Four-state visitor-entry <Moore machine> with a one-clock <output pulse>}
{description=Original state diagram. Edge labels use $x_1x_0$. State I emits the count pulse; its transitions can accept the next visitor without an extra idle clock.}
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