Analyzing the House Positions

There are three houses in a row. Let's label the positions from West to East as 1, 2, and 3.

We are given two key pieces of information:

• The middle sister does not live in the middle house (position 2). This means the middle sister lives in either position 1 or position 3.
• In the morning, the sun is in the East. Shadows fall towards the West. The shadow of the eldest sister's house falls on the youngest sister's house. This implies the eldest sister's house is located to the East of the youngest sister's house.

Deducing Possible Arrangements

Based on the shadow information, the eldest sister must be positioned East relative to the youngest sister. Let's examine the possible arrangements:

Scenario 1: Middle Sister lives in Position 1

If the middle sister occupies position 1, the remaining positions (2 and 3) must be occupied by the youngest and eldest sisters.

Since the eldest sister's house is East of the youngest sister's house, the arrangement must be:

• Position 1: Middle Sister
• Position 2: Youngest Sister
• Position 3: Eldest Sister

In this scenario, the youngest sister lives in the middle house (position 2).

Scenario 2: Middle Sister lives in Position 3

If the middle sister occupies position 3, the remaining positions (1 and 2) must be occupied by the youngest and eldest sisters.

Since the eldest sister's house is East of the youngest sister's house, the arrangement must be:

• Position 1: Youngest Sister
• Position 2: Eldest Sister
• Position 3: Middle Sister

In this scenario, the eldest sister lives in the middle house (position 2).

Final Conclusion

The two possible valid arrangements show that either the youngest sister (Scenario 1) or the eldest sister (Scenario 2) lives in the middle house.

Therefore, it can be concluded for sure that either the youngest or the eldest sister lives in the middle.