# How do you find the average score in an archery competition?

The problem is as follows:

In an archery contest the television host says the following:

The scores in this round of competition are from 0 to 20. Charles has 2 points less than Marina. Lewis has 2 points more than Annie. Bradley had the lowest score which was more than 14. Charles scores higher than Annie and Victor. With this information. If everyone has different scores, what is the average grade for Victor and Charles?

The alternatives given in my book are as follows:

1. 17
2. 18
3. 16
4. 15

How exactly should I find this peculiar order of information? From what I could guess here is that there is an implicit clue which indicates that there aren't draws.

But other than placing Bradley in the bottom, it doesn't say much about him because it say that he has a score higher than 14.

Marina > Charles

Now about Charles which it says that he scores higher than Annie and Victor. I don't get it. I'm assuming that he has a score which cannot be the sum of Annie and Victor because that would be over 20 which is the maximum allowed.

Charles > Annie and Charles > Victor

Since it mentions Lewis having 2 points more than Annie this would mean.

Lewis > Annie

But I don't know how to bring all of this together. Can someone help me to fill the gap?

For reference this problem was obtained from my Reason and logic book from 2000s and it seems to be an adaptation from a reprinted copy of Martin Gardner's Puzzle carnival of the 1970s.

I'm not very savvy with ordering information, can this be solved using a logic grid?. It would help me a lot if this would include a step by step approach so I can see what's happening.

• Usually the starting point in such a problem is "everyone has different scores". If you see this kind of phrase, you should start by counting the people and the possible scores. "The scores in this round of competition are from 0 to 20" and "... lowest score which was more than 14" combined gives each score must be one of 15, 16, 17, 18, 19, and 20 (six choices), and there are also 6 people (Charles, Marina, Lewis, Annie, Bradley, Victor). This gives the most crucial information: every possible score must be taken by someone. Commented Jan 7, 2021 at 0:13

The answer is Charles has 18, Marina has 20, Lewis has 19 and Annie has 17, Victor has 16, Bradley has 15. The answer is 1 therefore with 17.

Reason, it fits all the statements.

The important point here is that Charles has to be 18, If he was more he could not be 2 less than Marina and if he was less, only Victor or Annie could not be less than him at most because since Bradley is more than 14 this would mean that there would be at most one number between him and Charles. Once this is established, the rest should not be difficult to work out.

The scores in this round of competition are from 0 to 20. Charles has 2 points less than Marina.

18 is two less than 20

Lewis has 2 points more than Annie.

Lewis had 19 and Annie 17

15 is greater than 14.

Charles scores higher than Annie and Victor.

18 is greater than 17 and 16.

With this information. If everyone has different scores, what is the average grade for Victor and Charles?

They all have different scores (18+16)/2 is 17.

OP's questions

I'm lost at why Charles cannot be less than 18? I'm getting that Victor, Annie and Bradley can be less than him.

First of all Bradley has to be 15 cannot be more than otherwise it will leave at most 4 scores available for 5 people and there needs to be five. So if Charles was 17 then there would be only one score available, namely 16, when two available scores are needed. Obviously if he was 16 no available scores are available.

But I'm lost at why you ruled out this possibility? How did you concluded that Lewis is higher than Charles?

So since Charles has to be 18 and Bradley 15, Anne being less than Charles and greater than Bradley has to be either 16 or 17, she could not be 16 otherwise Lewis would be 18, but we have established Charles is that and no scores are the same, so Anne cannot be 16 and has to be 17. If Anne is 17, Lewis is 19 since his score is 2 more than Anne.

• Any questions? Do you want me to clarify anything? Commented Jan 6, 2021 at 17:43
• I'm lost at why Charles cannot be less than 18? I'm getting that Victor, Annie and Bradley can be less than him. But I'm lost at why you ruled out this possibility? How did you concluded that Lewis is higher than Charles? I'm getting that Victor can only be 16 if the other options have been assigned, but as indicated I'm still lost with the clue in bold in my comment. Can you explain this better? Commented Jan 6, 2021 at 17:47
• Better now????? Commented Jan 6, 2021 at 18:05
• Also if you think my answer is correct, the green tick would be much appreciated. Commented Jan 6, 2021 at 18:09
• Thank you very much for doing so. I'm giving you my check mark. Commented Jan 6, 2021 at 18:21