In a linear seating arrangement, several persons face either north or south and like different cities. Given the following conditions:

- B sits at the fourth position from one of the ends.
- The person who likes Hamilton sits fourth to the left of B.
- The number of persons between B and the one who likes Hamilton is one more than the number of persons between E and the one who likes Hamilton.
- Exactly two persons sit between E and F.
- F neither likes Hamilton nor sits to the right of B.
- The person who likes Tokyo sits third to the left of F.
- B and F face opposite directions.
- K sits adjacent to both H and F.
- The immediate neighbors of K face the opposite direction to K.
- The number of persons between K and the one who likes Tokyo is a multiple of 3.
- The number of persons between H and J is three times the number of persons to the right of H.
- J sits to the left of F.
- Exactly one person sits between H and I.
- Exactly three persons sit between D and J.
- Only one person sits to the right of D.
- The person who likes Boston sits fourth to the left of D.
- Exactly one person sits between J and the one who likes Houston, who faces north.
- G sits second to the left of J, and both face the same direction.
- The person who likes Madrid sits third to the left of E.
- The person who likes Toronto sits second to the left of I.

Based on the above information, which of the following statements is/are true?

I. More than 20 persons sit in the row

II. J likes Boston city

III. An even number of persons sit between the one who likes Tokyo and the one who likes Houston

Question

In a linear seating arrangement, several persons face either north or south and like different cities. Given the following conditions:

- B sits at the fourth position from one of the ends.
- The person who likes Hamilton sits fourth to the left of B.
- The number of persons between B and the one who likes Hamilton is one more than the number of persons between E and the one who likes Hamilton.
- Exactly two persons sit between E and F.
- F neither likes Hamilton nor sits to the right of B.
- The person who likes Tokyo sits third to the left of F.
- B and F face opposite directions.
- K sits adjacent to both H and F.
- The immediate neighbors of K face the opposite direction to K.
- The number of persons between K and the one who likes Tokyo is a multiple of 3.
- The number of persons between H and J is three times the number of persons to the right of H.
- J sits to the left of F.
- Exactly one person sits between H and I.
- Exactly three persons sit between D and J.
- Only one person sits to the right of D.
- The person who likes Boston sits fourth to the left of D.
- Exactly one person sits between J and the one who likes Houston, who faces north.
- G sits second to the left of J, and both face the same direction.
- The person who likes Madrid sits third to the left of E.
- The person who likes Toronto sits second to the left of I.

Based on the above information, which of the following statements is/are true?

I. More than 20 persons sit in the row

II. J likes Boston city

III. An even number of persons sit between the one who likes Tokyo and the one who likes Houston

Accepted Answer

**Solution:**

1. From the given clues, the seating arrangement can be deduced as follows (arrows indicate facing direction):

```
I ---------------> (Toronto)
   |      H
   |      K
   |      F
   |
   E <------------ (Tokyo)
   |
   |      G <---- (Hamilton)
   |
   |      J <---- (Boston)
   |
   |      B <---- (Houston)
   |
   D
```

2. **Statement I:** "More than 20 persons sit in the row"
   - By counting the individuals in the arrangement, the total number is less than or equal to 10.
   - Therefore, Statement I is **false**.

3. **Statement II:** "J likes Boston city"
   - From the arrangement, J is associated with Boston.
   - Hence, Statement II is **true**.

4. **Statement III:** "Even number of persons sit between the one who likes Tokyo and the one who likes Houston"
   - Tokyo is liked by E, Houston by B.
   - Counting persons between E and B in the arrangement gives an even number.
   - Therefore, Statement III is **true**.

**Answer:** Both II and III are true, so option (a) is correct.

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