Henry Ernest Dudeney/Modern Puzzles/199 - Golf Competition Puzzle
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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?
- $\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.
Click here for solution
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