Five houses of five different colours (blue, green, yellow, red and violet), with equal space between every two adjacent houses, are constructed in a row facing north. Which coloured house is exactly in the middle of the row?

**Statements:**

(I) Green and yellow coloured houses are constructed at the extreme ends of the row.

(II) Violet and blue coloured houses are immediate neighbouring houses of green and yellow coloured houses, respectively.

Question

Five houses of five different colours (blue, green, yellow, red and violet), with equal space between every two adjacent houses, are constructed in a row facing north. Which coloured house is exactly in the middle of the row?

**Statements:**

(I) Green and yellow coloured houses are constructed at the extreme ends of the row.

(II) Violet and blue coloured houses are immediate neighbouring houses of green and yellow coloured houses, respectively.

Accepted Answer

**Solution:**

1. **Analyze Statement I:**
   - Green and yellow houses are at the extreme ends.
   - Possible arrangements:
     - Green, _, _, _, Yellow
     - Yellow, _, _, _, Green
   - This alone does not determine the middle house.

2. **Analyze Statement II:**
   - Violet is immediate neighbor of green.
   - Blue is immediate neighbor of yellow.
   - Without knowing the ends, exact positions cannot be fixed.

3. **Combine Statements I and II:**
   - Case A: Ends are Green and Yellow.
     - Violet next to Green → second house is Violet.
     - Blue next to Yellow → fourth house is Blue.
     - Remaining colour is Red in the middle.
     - Arrangement: Green, Violet, Red, Blue, Yellow.

- Case B: Ends are Yellow and Green.
     - Blue next to Yellow → second house is Blue.
     - Violet next to Green → fourth house is Violet.
     - Remaining colour is Red in the middle.
     - Arrangement: Yellow, Blue, Red, Violet, Green.

4. In both cases, the middle house is Red.

**Answer:** Data in Statements I and II together is sufficient to answer the question.

Answer

Answer

Answer