Sharon was playing darts. She threw six darts and all of them hit the target. Which of the following could be her score?

The target goes from 9 in the center, then 7, 5 , 3, and 1 on the outside ring.

Possible Scores: 4 17 56 28 29 31 50 8

Please give a quick explanation.

To determine Sharon's score, we need to understand the scoring system of the dartboard. The target consists of several rings, each with a specific point value. Since Sharon hit the target with all six darts, we can calculate her possible scores by summing up the point values of each individual dart.

The center of the target, which is numbered 9, is worth the most points. The next ring, moving outward, is worth 7 points, followed by 5, 3, and 1 on the outer ring.

Based on this information, we can consider each of the given scores and evaluate if they are possible. Let's go through them:

- 4: This is not a possible score because it exceeds the maximum value that can be achieved.
- 17: To achieve this score, Sharon would have needed to hit the center bullseye twice and one 7-point ring. As there are only six darts thrown, this score is not possible.
- 56: This score is not possible as it exceeds the maximum value.
- 28: To obtain this score, Sharon would need to hit the center bullseye twice and one 7-point ring. This score is impossible since only six darts were thrown.
- 29: This score is not possible as it exceeds the maximum value.
- 31: To achieve this score, Sharon would have needed to hit the center bullseye three times. As there are only six darts, this score is too high and not possible.
- 50: To obtain this score, Sharon would need to hit the center bullseye five times while also hitting one of the 7-point rings. As only six darts were thrown, this score is not possible.
- 8: This score is possible if Sharon hit the outer ring (1-point) four times and the 3-point ring twice.

From the given list, the only possible score for Sharon is 8.

You have six darts, each hitting an odd number, so the answer must be an even number, since adding any two odd numbers gives you an even number. With six darts all hitting the target, you cannot get a score less than 6 nor more than 54. I'll let you figure out about the scores that remain.

I hope this helps. Thanks for asking.