Seating Arrangement Deduction Process

This solution details the step-by-step process to solve the seating arrangement puzzle. We need to find who sits third to the right of U, given that everyone faces North and sits in a straight line with equal spacing.

Step 1: Initial Placement of W and U

We start by placing individuals based on the most direct clues:

• Clue: "W sits second from the left end." This places W at position 2. The line looks like: _ W _ ...
• Clue: "U sits second to the right of W." With W at position 2, U is placed two positions to the right, at position 4. The line now looks like: _ W _ U ...

Step 2: Placing P, R, and Q Based on Ends

Next, we use clues related to the ends of the line and relative positions of P, Q, and R:

• Clue: "R sits one of the extreme ends."
• Clue: "P sits immediate left of R." This means they are adjacent as P R.
• Since W is at position 2, the P R pair cannot be at the left end. Thus, R must be at the rightmost end (position N). P is therefore at position N-1.
• Clue: "Q sits third to the left of P." With P at position N-1, Q is at position (N-1) - 3 = N-4. The arrangement structure is now ... Q ... P R.
• Clue: "Seven persons sit between T and P." Since P is near the right end, T must be to the left of P. This implies the structure T _ _ _ _ _ _ P.
• Combining these, T's position is P's position minus 8 (7 people + P themselves = 8 steps). So, T is at (N-1) - 8 = N-9.
• We have relative positions: T at N-9, W at 2, U at 4, Q at N-4, P at N-1, R at N.
• We test possible values for N to satisfy these conditions and check for contradictions. A consistent scenario emerged with N=16.
• If N=16: R=16, P=15, Q=12, T=7 (16-9=7).
• The partial arrangement is: _ W _ U _ _ T _ _ _ _ Q _ _ P R

Step 3: Integrating T, S, V, X Clues

We now place the remaining people (T, S, V, X) using the remaining clues:

• Clue: "Two persons sit between U and T." U is at 4, T is at 7. The positions between them are 5 and 6. This fits.
• Clue: "X sits exactly between Q and U." U is at 4, Q is at 12. The midpoint position is $\frac{4 + 12}{2} = 8$. So, X is at position 8.
• Clue: "V sits second to the left of X." With X at 8, V is at position 8 - 2 = 6.
• Clue: "S sits second to the left of Q." With Q at 12, S is at position 12 - 2 = 10.
• All derived positions (W=2, U=4, V=6, T=7, X=8, S=10, Q=12, P=15, R=16) satisfy all the given conditions for N=16.

Step 4: Find Person Third Right of U

We need to find the person third to the right of U.

• U is located at position 4.
• The position third to the right of U is $4 + 3 = 7$.
• According to our final arrangement, the person at position 7 is T.

Final Seating Arrangement Summary

The determined positions are:

Therefore, T sits third to the right of U.