Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player
during $2n-1$ consecutive days. Every match has a winner and a loser. Show that it is possible to select a winning player each day without selecting the same player twice. \\ \\ \textit{Hint: Remember Hall's Theorem}
given that Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days.
this is going to be proved by contradiction
Let there be a winning player each day where same players wins twice, let n = 3
there are 6 tennis players and match occurs for 5days
from hall's theorem, let set n days where less than n players wining a day
let on player be loser which loses every single day in n days
so, players loose to n different players in n days
if he looses to n players then , n players are winner
but, we stated less than n players are winners in n days which is contradiction.
so,
we can choose a winning players each day without selecting the same players twice.
First you must convert the weight from pounds to kg. 50 pounds is 22.7kg. You divide 50 by 2.2 to get that. Then you woukd divide what was ordered by what you have on hand 1.5÷75x ml. It would equal 0.02.
