Assignments

12 students took the class, each completing some of the assignments. Can you determine which students completed which work?

1. Every student finished at least one assignment, but no student finished every assignment.
2. Every assignment was completed by at least one student, but no assignment was completed by every student.
3. Fran completed exactly two assignments.
4. Emily did not complete any pair of consecutive assignments.
5. Beth and Georgia completed the same number of assignments.
6. The assignments completed by Anne are a proper subset of the assignments completed by Emily, and Emily's assignments are a proper of subset of those completed by Katherine.
7. The number of students who completed the first assignment times the number of students who completed the second assignment equals 20.
8. Joan completed two more assignments than Helen did.
9. Caroline completed exactly three assignments; the two she didn't do were consecutive.
10. Denise and Ione were perfect opposites--any assignment finished by Denise was skipped by Ione, and vice versa.
11. When the students are listed alphabetically, in every pair of consecutive students (that is, Anne/Beth, Beth/Caroline, Caroline/Denise, et cetera), at least one completed the fourth assignment. The same is true of the fifth assignment.
12. Only four students completed exactly one of assignments 4 and 5.
13. An even number of students completed the third assignment.
14. Anne and Denise both completed the fifth (or least signficant) assignment; no other assignment was completed by both of them.
15. The first (or most significant) assignment was completed by four students, all between Caroline and Georgia (inclusive) alphabetically.
16. Leah completed the second assignment if and only if Anne did not complete the fourth.
17. If you think of the assignments as a binary number, where finishing an assignment is a 1 and not finishing is a 0 (but why would you?), then Beth's number is the only palindrome.
18. Either Anne and Ione both completed exactly one assignment, or they both completed the second assignment.
19. Of Emily, Fran, and Georgia, exactly one did not complete the fourth assignment.
20. Either Leah completed all of the odd numbered assignments OR Ione completed exactly one of the first and second assignments.
21. Beth completed the second assignment; all of the other students who did so form one contiguous segment of the class when listed alphabetically.
22. The assignments completed by Katherine form a consecutive block.
23. The number of students who completed the fourth assignment plus the number who completed the fifth assignment equals 16.

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