24. In a tournament each of the six teams plays one match against every other team. In each round of matches, three take place simultaneously. A TV station has already decided which match it will broadcast for each round, as shown in the diagram. In which round will team $\mathrm{S}$ play against team U?
A 1
B 2
C 3
D 4
E 5
Solution
A

Consider team $P$. We are told the timing of three of its matches, against teams $Q, T$ and $R$ in rounds 1,3 and 5 respectively. This leaves fixtures against teams $U$ and $S$ to be fixed in rounds 2 or 4 and, since we are given that team $U$ is due to play team $T$ in round 4 , team $P$ plays team $S$ in round 4 and team $U$ in round 2 . The missing fixtures in rounds 2 and 4 can then be added to give the partial fixture list shown below.
Now consider team $T$. Fixtures against teams $P, Q$ and $U$ are now fixed in rounds 3.2 and 4 and, since team $R$ is unavailable in round 5 , team $T$ plays against team $R$ in round 1 and against team $S$ in round 5 . Therefore the missing fixture in round 1 is team $S$ against team $U$ and the complete fixture list can then be completed, as shown below.
Hence team $S$ plays team $U$ in round 1 .