Six arrows land on the target shown on the right [ring numbers: 3, 5, 7].
Each arrow is in one of the rings of the target. Which of the following of total scores is possible: 16, 19, 26, 31, 41, 44
well, 18 is the minimum
42 is the maximum
the sum of six odd numbers must be even
So only 26 is left.
I suppose 26 is the maximum.
Why did the arrows go on strike? Because the target wasn't paying them enough points! Let's see which scores are possible.
16: Hmm, let's see if we can hit that. If we get a 3, a 7, and two 3s, we're at 16. That's possible!
19: Alright, here we go. We can try a 7, a 7, and two 3s. That adds up to 20, not 19. So, it's not possible.
26: Let me do some quick math. If we get a 7, a 7, a 7, and a 5, we have a grand total of...26! Possible!
31: Now we're getting into the tricky territory. I'm not seeing any combination of 3s, 5s, and 7s that adds up to 31. Sorry, not possible.
41: Let's give this one a shot. If we get two 7s and four 7s, we have...28, not 41. Nope, not possible.
44: This is our last chance. If we get three 7s and three 7s...we're still at 42. So, 44 is not possible either.
So, the possible scores are 16 and 26.
26
41
To get the answer, try different combinations of 3, 5, and 7. The answer is 41.
To determine the possible total scores, we need to consider the values of the arrows and their corresponding ring numbers.
Based on the information given, we know that the ring numbers of the arrows are 3, 5, and 7. We can calculate the total score by adding up the values of these arrows.
Let's calculate the total scores for the given options:
- For a total score of 16, we need to find a combination of two arrows whose values add up to 16. However, since the given ring numbers are 3, 5, and 7, it is not possible to achieve a total score of 16.
- For a total score of 19, we can add the arrows with values 3, 3, and 7. This gives us a total score of 13. However, we have one arrow remaining whose value is either 3, 5, or 7. Adding any of these three would exceed the total score of 19. So, a total score of 19 is not possible.
- For a total score of 26, we can add the arrows with values 3, 7, and 7. This gives us a total score of 17. Adding another arrow with a value of 3 would give us a total score of 20. However, we have one arrow remaining whose value is either 3, 5, or 7. Adding any of these three would exceed the total score of 26. So, a total score of 26 is not possible.
- For a total score of 31, we can add the arrows with values 3, 7, and 7. This gives us a total score of 17. Adding another arrow with a value of 7 would give us a total score of 24. We have two arrows remaining whose values are either 3 or 5. Adding both of them would give us a total score of 31. So, a total score of 31 is possible.
- For a total score of 41, we can add the arrows with values 7, 7, and 7. This gives us a total score of 21. We have three arrows remaining whose values are either 3 or 5. Adding all three of them would give us a total score of 36. Since we can't reach 41 by adding any remaining arrow, a total score of 41 is not possible.
- For a total score of 44, we can add the arrows with values 7, 7, and 7. This gives us a total score of 21. We have three arrows remaining whose values are either 3 or 5. Adding all three of them would give us a total score of 36. Since we can't reach 44 by adding any remaining arrow, a total score of 44 is not possible.
From the given options, the possible total scores are 31.