Henry Ernest Dudeney/Puzzles and Curious Problems/317 - The Archery Match

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?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Crossing River Problem, and Problems Concerning Games and Puzzle Games: $317$. -- The Archery Match
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $467$. The Archery Match