Nine cross country runners compete in a team competition in
which there are three matches.
In the first match team X races
against team Y, in the second it is team Y against team Z and in
the third it is team Z against team X.
The runners are A, B, C, D,
E, F, G, H and I and in all the matches, when they run, they finish
in this order.
The teams are team X with runners A, F and H; team Y
with runners B, D and I; and team Z with runners C, E and G.
each match all the runners finish the course and 21 points are
awarded, 6 points to the first, 5 to the second, 4 to the third and
The judges work out the results of each of the three matches
and try to decide on the winning team for the competition overall.
If you were a judge what would you decide and what is peculiar
about the mathematics involved in this?