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

Modern Puzzles by Henry Ernest Dudeney: $199$

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?

$\qquad \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.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Problems Concerning Games: $199$. -- Golf Competition Puzzle
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $451$. Golf Competition Puzzle