Henry Ernest Dudeney/Puzzles and Curious Problems/317 - The Archery Match/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $317$
- The Archery Match
- On a target on which the scoring was $40$ for the bull's-eye, and $39$, $24$, $23$, $17$ and $16$ respectively for the rings from the centre outwards, as shown in the diagram,
- three players had a match with six arrows each.
- The result was:
- Miss Dora Talbot: $120$ points;
- Reggie Watson, $110$ points;
- Mrs. Finch, $100$ points.
- Every arrow scored, and the bull's-eye was only once hit.
- Can you, from these facts, determine the exact six hits made by each competitor?
Solution
Mrs. Finch scored $100$ with four $17$s and two $16$s.
Reggie Watson scored $110$ with two $23$s and four $16$s.
Miss Dora Talbot scored $120$ with one $40$ and five $16$s.
There are other ways to make $120$, but only one which uses the bull's-eye.
This is the only way the bull's-eye can be used and still fit the constraints of the question.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $317$. -- The Archery Match
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $467$. The Archery Match