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It is shown that the obvious necessary condition \(\lambda h(h – 1)m^2 \equiv 0 \pmod{k}\) for the existence of a \((v, k, \lambda)\)-perfect Mendelsohn design with \(h\) holes of size \(m\) is sufficient in the case of block size three, except for a nonexisting \((6, 3, 1)\)-PMD.