  In 2001, Zhongmin Shen asked if it is possible for two projectively related
Finsler metrics to have the same Riemann curvature tensor, [14, page 184]. In
this paper, we provide an answer to this question, within the class of Finsler
metrics of scalar flag curvature. In Theorem 3.1, we show that the answer is
negative, for non-vanishing scalar flag curvature. The answer is known to be
positive when the scalar flag curvature vanishes, [12, 14] and this positive
answer is related to the existence of many solutions to Hilbert's Fourth
Problem.
  As a generalisation of this problem, we can ask if it is possible for a given
spray, with non-vanishing scalar flag curvature, to represent, after
reparametrisation, the geodesic spray of a Finsler metric. In Proposition 3.3,
we show how to construct sprays whose projective class does not contain any
Finsler metrizable spray with the same Riemann curvature tensor.
