Solution Breakdown

To find the second shortest house, we must determine the height ranking of all six houses from 1 (tallest) to 6 (shortest).

Step 1: Determine the Tallest and Shortest Houses

• The clue "T, the tallest house..." directly tells us that T is Rank 1 (Tallest).
• The clue "The shortest house is exactly opposite to the green coloured house" requires a bit more work. By combining other clues, we can determine that house Q is green and it is opposite house U. Therefore, U is Rank 6 (Shortest).

Step 2: Use the Relative Height Clue

The final clue provides the key relationship for the remaining houses: "P, the white coloured house is taller than R, but shorter than S and Q."

This establishes the height order: (S and Q) > P > R.

Step 3: Establish the Full Height Ranking

We now fit the remaining four houses (P, Q, R, S) into the available ranks (2, 3, 4, 5).

• Since R is shorter than P, S, and Q, it must take the lowest available rank, which is 5. So, R is the 5th house in height.
• P is taller than R but shorter than S and Q, so it must take the next available rank. P is the 4th house.
• S and Q are the tallest in this group, so they occupy ranks 2 and 3 (the exact order between them cannot be determined, but it is not needed for this question).

Final Ranking

The complete height order from tallest to shortest is:

1. Tallest: T
2. S / Q
3. Q / S
4. P
5. Second Shortest: R
6. Shortest: U

The second shortest house is the one at rank 5, which is R.