In a soccer league with 6 teams $(P, Q, R, S, T, W)$, each team must eventually play each other team exactly once. So far, $P$ has played one match, $Q$ has played 2 matches, $R$ has played 3 matches, $S$ has played 4 matches, and $T$ has played 5 matches. How many matches has $W$ played so far?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Since $T$ has played 5 matches so far, then $T$ has played $P, Q, R, S$, and $W$ (ie. each of the other teams).

Since $P$ has played only 1 match and has played $T$, then $P$ has played no more matches.

Since $S$ has played 4 matches and has not played $P$, then $S$ must have played each of the remaining 4 teams (namely, $Q, R, T$, and $W$ ).

Since $Q$ has played only 2 matches and has played $T$ and $S$, then $Q$ has played no more matches. Since $R$ has played 3 matches, has played $T$ and $S$ but has not played $P$ or $Q$, then $R$ must have played $W$ as well.

Therefore, $W$ has played $T, S$ and $R$, or 3 matches in total. (Since we have considered all possible opponents for $W$, then $W$ has played no more matches.)

ANsweR: (C)