# Can you follow this solution to a recreational math problem?

I have a Web page for high school level math. Part of the site is a collection of recreational problems. I recently came across a problem in a book that I would like to include. I give due credit to the author for the problem and give my technique for solving it, which is different from that given in the book. The solution mostly requires knowledge of nothing more than basic arithmetic, but I am afraid that it might still be difficult to follow. If you have a few minutes to spare, I would appreciate your feedback before I decide whether to use the problem. The problem

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No. I was tripped right away by this:

The possible scores for a given throw are 1, 5, 10, 25, 50 and 100. Given that each score is achieved by exactly one of the players.and that the sum of the scores of each player is the same, what are the scores of each player?

“Given that each score is achieved by exactly one of the players”: From this I understood that only one player scored the 1’s.

I also don’t see in the description a requirement that anyone score 1’s. Where does it say that each score must be achieved at all?

I’m not a math person, and I never do such puzzles for fun. There’s nothing recreational about them for me; they bring tears to my eyes and panic to my breath. But I do think I can read and write plain English, and that’s the test I applied here.

Can we improve on this? If 100, 50 and 25 are scored by two players, the MinMaxScore is at most 10

This made me think I’d misunderstood the requirement and that more than one player could make a given score.

the third highest MaxScore, which will be called the MinMaxScore, is at most 25, which willl be the case when 100, 50 and 25 are each thrown by different players.

I can tell you that there’s a typo in “will.”

Maybe you can use the problem after a little rewriting.

Don’t bother to try to explain to me because I’m not willing to bend my head to it as much as that; but it should be unambiguous to your students.

Jeruba (50453)

This doesn’t make sense: Given that each score is achieved by exactly one of the players.and that the sum of the scores of each player is the same, what are the scores of each player? As a start, show that there must be five 1’s, which is a crucial part of the solution in the book and in the solution given here.

How can each score be achieved by only one player, but the scores be the same? Please explain the scoring of the game more clearly.

zenvelo (35262)

I see the problem. I need to distinguish the number of points on a single throw from the total score. The book describes it this way: “No number of points scored by a dart was scored by more than one person.” Is that clearer? The idea is that one person scored all the 1’s, one person scored all the 5’s, etc.

Get rid of any ambiguity over whether “score” means points on a single throw or total points. Define the term up front and use it to mean only one thing.

The three sets of scores are:
Nine 25’s
Four 50’s and five 1’s
Two 100’s, two 10’s and five 1’s

Jeruba (50453)

It should be Four 50’s and five 5’s

Yes, but the question is a mundane exercise in substitution.

Pinguidchance (5017)