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

- Every student finished at least one assignment, but no student finished every assignment.
- Every assignment was completed by at least one student, but no assignment was completed by every student.
- Fran completed exactly two assignments.
- Emily did not complete any pair of consecutive assignments.
- Beth and Georgia completed the same number of assignments.
- 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.
- The number of students who completed the first assignment times the number of students who completed the second assignment equals 20.
- Joan completed two more assignments than Helen did.
- Caroline completed exactly three assignments; the two she didn't do were consecutive.
- Denise and Ione were perfect opposites--any assignment finished by Denise was skipped by Ione, and vice versa.
- 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. - Only four students completed exactly one of assignments 4 and 5.
- An even number of students completed the third assignment.
- Anne and Denise both completed the fifth (or least signficant) assignment; no other assignment was completed by both of them.
- The first (or most significant) assignment was completed by four students, all between Caroline and Georgia (inclusive) alphabetically.
- Leah completed the second assignment if and only if Anne did not complete the fourth.
- 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.
- Either Anne and Ione both completed exactly one assignment, or they both completed the second assignment.
- Of Emily, Fran, and Georgia, exactly one did not complete the fourth assignment.
- Either Leah completed all of the odd numbered assignments OR Ione completed exactly one of the first and second assignments.
- Beth completed the second assignment; all of the other students who did so form one contiguous segment of the class when listed alphabetically.
- The assignments completed by Katherine form a consecutive block.
- The number of students who completed the fourth assignment plus the number who completed the fifth assignment equals 16.

First | Second | Third | Fourth | Fifth | |
---|---|---|---|---|---|

Anne | |||||

Beth | |||||

Caroline | |||||

Denise | |||||

Emily | |||||

Fran | |||||

Georgia | |||||

Helen | |||||

Ione | |||||

Joan | |||||

Katherine | |||||

Leah |