pts) In a round-robin tennis tournament of players, everyplayer plays against every other
player exactly once and there is no draw. We call a player x adominator if for every other player y
either x has beaten y directly or x has beaten some player whohas beaten y. By using mathematical
induction, prove that for each integer n ? 2 at anyround-robin tournament of n players, one can
always find a dominator.
In case 3, suppose there is no such z. This means that anyplayer that
x has beaten a also has beaten. Now, why does that mean a isfor sure
a dominator among the k+1 players? You will need to supplydetails rather
than just stating so. Let's think what would it require for ato be a dominator.
This means if I hand you any player y (besides a and x), thenyou must argue to me
that either a has beaten y or there is a player z such that abeat z and z beat y.
Why must that be true? Remember x is a dominator among the kplayers other
than a. So what do we know about x versus y? and how does thattranslate into
a versus y? (remember the observation we made earlier about xand a),
Please think a bit harder. If you would like to revise yoursolution you can rewrite
a solutiion and e-mail it to me by Monday noon. Please usethis opportunity to think
