Question 3 in ps.11 possible mistake in solution

question 3 in ps11 section b
the section asks “how many registers are required by the design” which is 1
the answer in ps.11 solution refers to the amount of the flipflops
but even there comes up another
problem which is that there is n+1 flipflops (n-flipflops in the register and another one that acts as the selector bit actuator )
but the suggested answer is n flipflops.

please refer to the solution in question 2 in the moodle in 2016_Fall_MoedA_sol.pdf
the number of FF is 1 for the clock and n more for the register, a total of n+1