Seven persons P, Q, R, S, T, U, and V study in three different universities: Oxford, Cambridge, and Texas. Each person likes a different colour: Brown, Grey, Green, White, Maroon, Silver, and Gold. The following conditions apply:

- Minimum two but not more than three persons study in the same university.
- P likes Brown but does not study in Texas.
- T studies only with Q but they do not study in Texas.
- S and the one who likes White study in the same university.
- V and the one who likes Maroon study in the same university.
- The ones who like Grey and Green study neither in the same university nor in Texas.
- T does not study in Oxford.
- The ones who like Silver and Grey study in the same university.
- V studies with more than one person.
- Q does not like Silver.
- R does not study in Oxford.
- R does not like Gold and Maroon.
- S and U do not like Gold.

**Question:** Who among the following studies in Cambridge and likes Grey colour?

Question

Seven persons P, Q, R, S, T, U, and V study in three different universities: Oxford, Cambridge, and Texas. Each person likes a different colour: Brown, Grey, Green, White, Maroon, Silver, and Gold. The following conditions apply:

- Minimum two but not more than three persons study in the same university.
- P likes Brown but does not study in Texas.
- T studies only with Q but they do not study in Texas.
- S and the one who likes White study in the same university.
- V and the one who likes Maroon study in the same university.
- The ones who like Grey and Green study neither in the same university nor in Texas.
- T does not study in Oxford.
- The ones who like Silver and Grey study in the same university.
- V studies with more than one person.
- Q does not like Silver.
- R does not study in Oxford.
- R does not like Gold and Maroon.
- S and U do not like Gold.

**Question:** Who among the following studies in Cambridge and likes Grey colour?

Accepted Answer

**Solution:**

1. **Universities and group size:** There are 7 persons divided into 3 universities: Oxford, Cambridge, Texas. Each university has at least 2 and at most 3 persons.

2. **Given conditions:**
   - P likes Brown and does not study in Texas.
   - T studies only with Q, and both are not in Texas.
   - S and the one who likes White study in the same university.
   - V and the one who likes Maroon study in the same university.
   - Grey and Green likers study neither in the same university nor in Texas.
   - T does not study in Oxford.
   - Silver and Grey likers study in the same university.
   - V studies with more than one person.
   - Q does not like Silver.
   - R does not study in Oxford.
   - R does not like Gold or Maroon.
   - S and U do not like Gold.

3. **Stepwise deduction:**

- Since T studies only with Q and both are not in Texas, and T does not study in Oxford, T and Q must be in Cambridge.

- Silver and Grey likers study in the same university. Q does not like Silver, so Q must like Grey, and T must like Silver.

- Grey and Green likers do not study in the same university or in Texas. Since Q likes Grey and is in Cambridge, Green liker cannot be in Cambridge or Texas, so Green liker must be in Oxford.

- P likes Brown and does not study in Texas, so P is in Oxford.

- V studies with more than one person and with the one who likes Maroon. So V and Maroon liker are in the same university with at least 3 persons.

- S and the one who likes White study in the same university.

- R does not study in Oxford and does not like Gold or Maroon.

- S and U do not like Gold.

4. **Assigning persons to universities and colours:**

- Oxford (3 persons): P (Brown), U (Green), and one more.
   - Cambridge (3 persons): Q (Grey), T (Silver), R (White).
   - Texas (1 person): S (Maroon), V (Gold).

But Texas must have minimum 2 persons, so Texas must have 2 or 3 persons.

Since V studies with more than one person and with Maroon liker, V and S are in Texas.

So Texas has S (Maroon) and V (Gold).

Oxford has P (Brown), U (Green), and one more (not R, since R is not in Oxford).

Cambridge has Q (Grey), T (Silver), R (White).

5. **Final arrangement:**

| University | Person | Colour  |
|------------|---------|---------|
| Oxford     | P       | Brown   |
| Oxford     | U       | Green   |
| Oxford     | (Leftover) | (Leftover) |
| Cambridge  | Q       | Grey    |
| Cambridge  | T       | Silver  |
| Cambridge  | R       | White   |
| Texas      | S       | Maroon  |
| Texas      | V       | Gold    |

Since all 7 persons are accounted for, the leftover in Oxford is none (only 2 persons there).

**Answer:** Q studies in Cambridge and likes Grey colour.

**Answer:** Q

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