Fifteen people are standing in a straight line facing north. What is the position of M with respect to S?

I. P is standing third from the left end of the row. There are exactly two people between P and M. N is positioned third to the right of M. S is an immediate neighbor of N.

II. Q is standing second from the right end of the row. There are exactly two people between Q and O. O is an immediate neighbor of S. The number of people to the left of M is equal to the number of people to the right of S.

Question

Fifteen people are standing in a straight line facing north. What is the position of M with respect to S?

I. P is standing third from the left end of the row. There are exactly two people between P and M. N is positioned third to the right of M. S is an immediate neighbor of N.

II. Q is standing second from the right end of the row. There are exactly two people between Q and O. O is an immediate neighbor of S. The number of people to the left of M is equal to the number of people to the right of S.

Accepted Answer

**Solution:**

1. From statement I:
   - P is third from the left end.
   - There are two people between P and M, so M can be either 6th or 1st from the left.
   - N is third to the right of M.
   - S is an immediate neighbor of N.

However, this information alone is not enough to determine M's exact position relative to S.

2. From statement II:
   - Q is second from the right end.
   - There are two people between Q and O.
   - O is an immediate neighbor of S.
   - The number of people to the left of M equals the number of people to the right of S.

This also does not provide enough information alone to find M's position with respect to S.

3. Combining both statements:
   - Using the positions of P, M, N from statement I and the relative positions of Q, O, S from statement II along with the equality condition of people on either side of M and S, we can deduce the exact positions.

Therefore, both statements together are necessary to answer the question.

**Answer:** The data in both statement I and II together are necessary to answer the question.

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