A certain number of persons are seated in a straight line, all facing north. The following conditions are given:
- P sits third to the right of S. - Exactly three persons sit between P and Q. - U sits third to the left of Q. - U is seated fifth from the left end of the row. - R sits third to the left of U. - Exactly three persons sit between W and T, and T is an immediate neighbor of R. - Exactly six persons sit to the right of W. - M sits immediately to the left of O. - Exactly three persons sit between M and H. - O does not sit to the left of P. - H is not seated at either extreme end of the row.
How many persons are seated in the row?

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**Solution:**

1. Since U is fifth from the left end, place U at position 5.

2. R sits third to the left of U, so R is at position 2 (5 - 3 = 2).

3. T is an immediate neighbor of R and three persons sit between W and T. Since T neighbors R at position 2, T can be at position 1 or 3.

4. If T is at position 1, then W must be at position 5 (1 + 4), but position 5 is occupied by U. So T must be at position 3.

5. With T at 3, W is at position 7 (3 + 4), because three persons sit between W and T.

6. Exactly six persons sit to the right of W, so total number of persons = position of W + 6 = 7 + 6 = 13.

7. P sits third to the right of S, so if S is at position x, P is at x + 3.

8. Exactly three persons sit between P and Q, so the distance between P and Q is 4 positions.

9. U sits third to the left of Q, so Q is at position 8 (U at 5 + 3).

10. Using these, place S at position 5 (since P would be at 8), but 5 is occupied by U, so try S at position 4, then P at 7.

11. O does not sit to the left of P (P at 7), so O must be at position 7 or greater.

12. M sits immediately to the left of O, so M is at position O - 1.

13. Exactly three persons sit between M and H, and H is not at an extreme end.

14. By placing M and O at positions 9 and 10 respectively, H can be at position 5 or 13, but 5 is occupied by U and 13 is an extreme end, so H must be at position 6.

15. All conditions are satisfied with 13 persons in the row.

**Answer:** 13

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