D(2,3,4),D(1,3,5), or
2z,;zy,;yx,;xa,;2w,;wb,;2v,;vu,;uc,;2t,;td,;2e,;edc,2ba,;
has nim-value *10, while
D(2,3,4),D(1,5,3), or
2z,;zy,;yx,;xa,;2w,;wb,;2v,;vu,;uc,;2t,;td,;2e,;edc,2ab,;
has nim-value *8.
I have not made a detailed examination of the proof that this is
impossible, so I don't know where it fails. If anyone wants a
detailed list of the nim-values I calculated in arriving at this
counterexample, just ask.
Dan