Editing Betweenness problem (section)

==Examples==
As an example, the collection of input triples
:(2,1,3), (3,4,5), (1,4,5), (2,4,1), (5,2,3)
is satisfied by the output ordering
:3, 1, 4, 2, 5
but not by
:3, 1, 2, 4, 5.
In the first of these output orderings, for all five of the input triples, the middle item of the triple appears between the other two items 
However, for the second output ordering, item 4 is not between items 1 and 2, contradicting the requirement given by the triple (2,4,1).

If an input contains two triples like (1,2,3) and (2,3,1) with the same three items but a different choice of the middle item, then there is no valid solution. However, there are more complicated ways of forming a set of triples with no valid solution, that do not contain such a pair of contradictory triples.