Question 12
School exams must be scheduled over five available days, Day 1 to Day 5. Each exam is a circle. Two circles are connected exactly when the exams share candidates and therefore must occur on different days. Follow these rules:
1. Connected exams cannot use the same day.
2. Schedule exams with more connections before those with fewer.
3. Always use the earliest possible day: try Days 1, 2, 3, 4, then 5.
4. Aim to use as few days as possible.
For example, three exams, one conflicting with both others, need at least two days:
For these seven exams, what is the minimum number of days, and what is the greatest number of exams held on one day in that schedule?
1. Connected exams cannot use the same day.
2. Schedule exams with more connections before those with fewer.
3. Always use the earliest possible day: try Days 1, 2, 3, 4, then 5.
4. Aim to use as few days as possible.
For example, three exams, one conflicting with both others, need at least two days:
For these seven exams, what is the minimum number of days, and what is the greatest number of exams held on one day in that schedule?