Ten persons — M, N, O, P, Q, T, U, V, W, and X — are seated around a circular table, not necessarily in the given order. Five face inward, and the other five face outward. The following conditions apply:

- No two persons with consecutive alphabetical names sit next to each other.
- Not more than two neighbors face the same direction.
- Exactly two persons sit between W and N.
- M sits third to the right of N.
- Immediate neighbors of M face opposite directions.
- X and V sit immediately to the left of each other but are not immediate neighbors of N.
- O and P sit second to the right of each other.
- No one sits between O and X on either side.
- Immediate neighbors of U face the same direction, which is opposite to U's direction.
- W and Q face the same direction.
- X does not face outside.

**Question:** The number of persons sitting between N and W when counted to the left of W is equal to the number of persons sitting between which two persons when counted to the left of the latter?

Question

Ten persons — M, N, O, P, Q, T, U, V, W, and X — are seated around a circular table, not necessarily in the given order. Five face inward, and the other five face outward. The following conditions apply:

- No two persons with consecutive alphabetical names sit next to each other.
- Not more than two neighbors face the same direction.
- Exactly two persons sit between W and N.
- M sits third to the right of N.
- Immediate neighbors of M face opposite directions.
- X and V sit immediately to the left of each other but are not immediate neighbors of N.
- O and P sit second to the right of each other.
- No one sits between O and X on either side.
- Immediate neighbors of U face the same direction, which is opposite to U's direction.
- W and Q face the same direction.
- X does not face outside.

**Question:** The number of persons sitting between N and W when counted to the left of W is equal to the number of persons sitting between which two persons when counted to the left of the latter?

Accepted Answer

**Solution:**

1. The problem involves seating 10 persons around a circular table with specific constraints on their seating order and facing directions.

2. Key points:
   - Two persons sit between W and N.
   - M is 3rd to the right of N.
   - Immediate neighbors of M face opposite directions.
   - X and V sit immediately to the left of each other but are not neighbors of N.
   - O and P are 2nd to the right of each other.
   - No one sits between O and X on either side.
   - Neighbors of U face the same direction, opposite to U.
   - W and Q face the same direction.
   - X faces inside (not outside).

3. From the condition "Two persons sit between W and N," when counting to the left of W, the number of persons between W and N is 2.

4. The question asks for another pair of persons with the same number of people sitting between them when counted to the left of the latter.

5. By carefully arranging the seating according to the conditions, it is found that the number of persons between V and Q when counted to the left of Q is also 2.

6. Therefore, the pair with the same count of persons between them as between W and N (to the left of W) is V and Q (to the left of Q).

**Answer:** (d) V and Q

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