Instructions

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.

The following additional facts are also known.

1. Seminars by students from Economics are scheduled in each of the four slots.

2. A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.

3. F is an Anthropology student whose seminar is scheduled at 10:30 am.

4. The seminar of a Sociology student is scheduled at 9:00 am.

5. B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.

6. P, who is guiding both B and C, has students scheduled in the first two slots.

7. A and G are scheduled in two consecutive slots.

Solution

Let's look at all the students we have A,B,C,D,E,F,G,H. The guides are P,Q,R,S,T and they mentor 2,1,2,1,2 students respectively.

Slots are 9:00,9:30,10:00,10:30 . Moreover economics, sociology and anthropology have 4,3,1 students respectively.

Now from 5th statement, two sociology seminars and economics seminars are held in the same slot. This will not take place at 10:00(only one seminar is scheduled at 10:00), this will also not take place at 10:30( An anthropology seminar is scheduled at 10:30 and maximum three seminars are scheduled in a slot. Hence this will happen at either 9 or 9:30. Now from (7) A and G are scheduled in consecutive slots. A is scheduled at 10:00. Hence G will be scheduled at 9:30. SO from (5), there will be three students having their seminars at 9:30.

Combining this data with the remaining points we get the following table

Moreover we do know that students having same subject are scheduled in consecutive slots. So we get

Here we can see that two seminars are scheduled in first slot.

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