True or False Quizes

[chocchief]

To offset the effect of guessing, true/false tests are often scored by subtracting the number of wrong answers from the number of right answers, with missed out questions not counted. Recently, a 30-item true/false test was scored like this, and Bill, Dot and 6 other students all got the same score, although no two of them answered the same number of questions. All eight belong to at least 2 of the 5 student clubs at their high school, but no two belong to the exactly the same combination of clubs. From the following clues, can you find the full name of each student (one last name is Mills), the clubs they belong to, the number of questions each answered correct and incorrect, and the score they got?

1. Neither Paul, who is not the Ross boy, nor Ali was the one who had no wrong answers.

2. No one belongs to both the Hiking and the Stamp club, or to both the Model Railroad and the Chess club.

3. The four Drama club members answered the largest number of items.

4. No one had more than 7 incorrect answers.

5. The Evans kid, who belongs to the Model Railroad Club but not Drama, answered more questions than everyone else who is not a member of the Drama Club.

6. Grace and the Leroy girl answered fewer items than the other Drama Club members.

7. Mike and the North girl between them represent all 5 clubs and have no club membership in common; the same is true of Paul and the Fisher youngster.

8. Of the Drama Club members, the two who also belong to the Model Railroad Club answered more questions than the two who also belong to the Chess Club.

9. The Clark girl, who answered 20 questions, and Karen, who answered 26, belong to two of the same clubs.

10. Of those who do not belong to Drama, the two in the Hiking Club answered more items than the two in the Stamp Club.

11. Joe who answered 28 questions (which was not the most), and the Horn youngster, who answered 18, belong to two of the same clubs.

[bonanova]

This is one of the best puzzles of this type I have seen.

It has several levels, and it is as demanding as puzzles

that have many more variables that are difficult only

because they are big.

chocchief, look forward to more if you have them.

Everyone scored 16 points, with 0 1 2 3 4 5 6 or 7 wrong answers.
Each club had four members
Four students belonged to three of them
Four students belonged to two of them

+-----+-----+-----+------+------+-----+-----+-----+-----+-----+-------+

|Score Wrong Total| First Last |Chess Drama Hike RailR Stamp| #clubs|

+-----+-----+-----+------+------+-----+-----+-----+-----+-----+-------+
| 16 7 30 | Mike Mills?| x O O O x | 3 |
| 16 6 28 | Joe Ross? | x O x O O | 3 |
| 16 5 26 | Karen Leroy | O O O x x | 3 |
| 16 4 24 | Grace Fisher| O O x x O | 3 |
| 16 3 22 | Paul Evans | x x O O x | 2 |
| 16 2 20 | Ali Clark | O x O x x | 2 |
| 16 1 18 | Bill Horn | x x x O O | 2 |
| 16 0 16 | Dot North | O x x x O | 2 |

+-----+-----+-----+------+------+-----+-----+-----+-----+-----+-------+

I'm not totally satisfied with my solution.
It seems that it could also be that Mike is Ross and Joe is Mills.

Does anyone see a clue that nails this down?

[Barcallica]

The same is true of Paul and the Fisher youngster. from clue 7 is not helping me

Edited June 8, 2013 by Barcallica

[Barcallica]

The same is true of Paul and the Fisher youngster. from clue 7 is not helping me

[DeGe]

Here's what I got

[bonanova]

It seems the OP allows all three of the above solutions.

Barcallica's Paul/Bill uncertainty is resolved using clue 7.

Nevertheless, Mills and Ross seem interchangeable.

DeGe's solution shows that {Mike and the North girl}

can be interchanged with {Paul and the Fisher youngster},

whose wrong answers can be either {7 0} and {3 4}

or v.v, respectively.

Sometimes the flavor text hides a clue, but not this time.

Great puzzle otherwise.

[DeGe]

DeGe's solution shows that {Mike and the North girl}

can be interchanged with {Paul and the Fisher youngster},

whose wrong answers can be either {7 0} and {3 4}

or v.v, respectively.

From what I remember while solving it, there were no unresolved elements and each piece fitted in one place only (I have now deleted the file that I used to work this out).

The interchangeability between Mike/North and Paul/Fisher is also resolved. I don't remember how exactly I resolved it but it had something to do with there being only 3 girls names... Grace, Karen, and Dot. In case of interchanging Paul/Fisher and Mike/North, some other condition was being violated.

[bonanova]

DeGe's solution shows that {Mike and the North girl}

can be interchanged with {Paul and the Fisher youngster},

whose wrong answers can be either {7 0} and {3 4}

or v.v, respectively.

From what I remember while solving it, there were no unresolved elements and each piece fitted in one place only (I have now deleted the file that I used to work this out).

The interchangeability between Mike/North and Paul/Fisher is also resolved. I don't remember how exactly I resolved it but it had something to do with there being only 3 girls names... Grace, Karen, and Dot. In case of interchanging Paul/Fisher and Mike/North, some other condition was being violated.

I hadn't thought of that, assuming Ali was short for Allison, who, in my social experience, is decidedly female.

I guess that wraps it up. Nice solve.

And since chocchief doesn't seem to be around, I'll mark it.