Oh! Snails

Four snails travel at uniform, rectilinear motion on a very large plane surface. The directions of their paths are random, (but not parallel, i.e. any two snails could meet), but no more than two snail paths can cross at any one point. Five of the \((4\times3)/2=6\) possible encouters have already occured. Can we state with certainty that the sixth encounter will also occur?


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