A directed triple system of orderv (or, DTS(v)) is a decomposition of the complete directed graph Kv→ into transitive triples. A v-good sequencing of a DTS(v) is a permutation of the points of the design, say [x1⋯xv], such that, for every triple (x,y,z) in the design, it is not the case that x=xi, y=xj and z=xk with i<j<k. We prove that there exists a DTS(v) having a v-good sequencing for all positive integers v≡0,1mod3. Further, for all positive integers v≡0,1mod3, v≥7, we prove that there is a DTS(v) that does not have a v-good sequencing. We also derive some computational results concerning v-good sequencings of all the nonisomorphic DTS(v) for v≤7.
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