Henry Ernest Dudeney/Modern Puzzles/199 - Golf Competition Puzzle

by : $199$

 * Golf Competition Puzzle
 * I was asked to construct some schedules for players in American golf competitions.
 * The conditions are:
 * $(1)$ Every player plays every player once, and once only.
 * $(2)$ There are half as many links as players, and every player plays twice on every links except one, on which he plays but once.
 * $(3)$ All the players play simultaneously in every round, and the last round is the one in which every player is playing on a links for the first time.
 * I have written out schedules for a long series of even numbers of players up to $26$,
 * but the problem is too difficult for this page except for in its most simple form -- for six players.
 * Can the reader, calling the players $A$, $B$, $C$, $D$, $E$, and $F$,
 * and pairing these in all possible ways, such as $AB$, $CD$, $EF$, $AF$, $BD$, $CE$, etc.,
 * complete this table for six players?


 * $\begin {array} {r | c |}

\text {Rounds} & 1 & 2 & 3 & 4 & 5 \\ \hline \text{$1$st Links} & &  &  &  & \\ \hline \text{$2$nd Links} & &  &  &  & \\ \hline \text{$3$rd Links} & &  &  &  & \\ \hline \end{array}$


 * For such a small number it is easy but interesting.