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Puzzle 31) The archery match

Submitted by Abhishek Jain, on September 30, 2017


In an archery match, scoring of target was 40 for the bull's-eye, 39 for the outer ring of bull’s eye, and 24,23, 17, and 16 respectively for the outer rings of one another respectively, as shown below.

The arhery match

Three players had a match with six arrows each. The result was: Marry, 120 points; Harry, 110 points; Larry, 100 points. Every arrow hits the target and scored, and the bull's-eye was hit only once.

Can you, from above facts, determine the exact six score/hit made by each competitor?

Key points

  • Scoring: 40 for bull’s eye and 39,24,23,17 and 16 respectively for the rings from the center outwards.
  • There are 3 players for a match with six arrows each.
  • Result: Marry : 120 points, Harry : 110 points, Larry: 100 points.
  • It is guaranteed that, every arrow hits the target.
  • The bull’s eye was hit only once.
  • You have to determine the exact six hits made by each competitor.


Mr. Larry scored 100 with four 17's and two 16's; Harry scored 110 with two 23's and four 16's; Marry scored 120 with one 40 and five 16's. Her score can be made up in various ways, except for the fact that the bull's-eye has to be got in somewhere, and this is the only place where it can occur.

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