At a class, the students are going to choose a leader. The class has 3 groups of students, and each group contains 4 students, so the total number of students is 12. After discussion, they determine the following rule:
each student has to vote 1 from each group (so each student has to vote for 3 persons).
For example, if the groups are [a,b,c,d] [e,f,g,h] [i,j,k,l], then each student has to choose 1 from [a,b,c,d], 1 from [e,f,g,h], and 1 from [i,j,k,l].
If someone breaks the rules, their vote is disqualified.
(To simplify the problem, let's write just the initials of the students, since no 2 students have the same initials.)
Here are the votes:
1. [c,d,f] 2. [a,g,c] 3. [d,h,l] 4. [b,e,d] 5. [f,j,g] 6. [g,j,i] 7. [j,i,a] 8. [j,a,f] 9. [b,h,k] 10.[l,c,d] 11.[a,h,l] 12.[g,e,b]
There is 1 vote which is disqualified.
- Determine each group's members.
- Determine which vote is disqualified.