Seating Arrangement Setup

The problem describes a seating arrangement with ten people in two parallel rows. Each row has five people. Row 1 contains J, K, L, M, and N, all facing South. Row 2 contains V, W, X, Y, and Z, all facing North. This means individuals in one row face individuals in the opposite row directly across.

Deriving the Seating Arrangement

We will deduce the seating positions step-by-step using the given clues:

1. Row 2 Clues:
   • "Z sits third to the right of W." Since they face North, if we number seats 1 to 5 from left to right, this means there are two people between W and Z, with Z to W's right. Possible placements are W _ _ Z _ (W at 1, Z at 4) or _ W _ _ Z (W at 2, Z at 5).
   • "V sits second to the left of Z."
     • If W is at 1 and Z is at 4 (W _ _ Z _), the second seat to the left of Z (pos 4) is position 2. So, V is at position 2. Arrangement: W V _ Z _. (W=1, V=2, Z=4).
     • If W is at 2 and Z is at 5 (_ W _ _ Z), the second seat to the left of Z (pos 5) is position 3. So, V is at position 3. Arrangement: _ W V _ Z. (W=2, V=3, Z=5).
2. Row 1 Clues linked to Row 2:
   • "The person facing V sits to the immediate right of K." (Remember, Row 1 faces South).
     • Case 1 (Row 2: W V _ Z _): V is at position 2. The person facing V is at position 2 in Row 1. Let's call this person P2. P2 is to the immediate right of K. Since Row 1 faces South, "right" means lower seat numbers. Thus, K must be at position 1, and P2 (facing V) is at position 2. Row 1 starts: K P2 _ _ _.
     • Case 2 (Row 2: _ W V _ Z): V is at position 3. The person facing V is at position 3 in Row 1 (P3). P3 is to the immediate right of K. So, K must be at position 2, and P3 (facing V) is at position 3. Row 1 starts: _ K P3 _ _.
   • "Only one person sits between K and M."
     • Case 1 (Row 1: K P2 _ _ _): K is at 1. One person between K and M means M is at position 3. Row 1: K P2 M _ _. P2 can be L, N, or J (P2 cannot be M).
     • Case 2 (Row 1: _ K P3 _ _): K is at 2. One person between K and M means M is at position 4. Row 1: _ K P3 M _. P3 can be L, N, or J (P3 cannot be M).
   • "J is not an immediate neighbor of K."
     • Case 1 (Row 1: K P2 M _ _): K is at 1. J cannot be at position 2 (P2). So J must be at position 4 or 5.
       • If J=4: K P2 M J _. N must be P2 or 5. N cannot be P2. So N=5. Row 1: K P2 M J N. P2 must be L. Row 1: K L M J N.
       • If J=5: K P2 M _ J. N must be P2 or 4. N cannot be P2. So N=4. Row 1: K P2 M N J. P2 must be L. Row 1: K L M N J.
     • Case 2 (Row 1: _ K P3 M _): K is at 2. J cannot be at position 1 or P3 (pos 3). M is at 4. So J must be at position 5. Row 1: _ K P3 M J. N must be P3 or position 1. N cannot be P3. So N=1. Row 1: N K P3 M J. P3 must be L. Row 1: N K L M J.
   • "Only two people sit between J and L."
     • Check Case 1 possibilities:
       • Row 1: K L M J N (K=1, L=2, M=3, J=4, N=5). J(4) and L(2). Between them is M(3) - only 1 person. Invalid.
       • Row 1: K L M N J (K=1, L=2, M=3, N=4, J=5). J(5) and L(2). Between them are M(3) and N(4) - 2 people. Valid.
     • Check Case 2 possibility:
       • Row 1: N K L M J (N=1, K=2, L=3, M=4, J=5). J(5) and L(3). Between them is M(4) - only 1 person. Invalid.

   Thus, Case 1 yields the only valid Row 1 arrangement: K L M N J (South).

3. Finalizing Row 2:
   • From step 1, Case 1 gave Row 2 as W V _ Z _. Positions: W=1, V=2, Z=4.
   • The remaining persons for Row 2 are X and Y, occupying positions 3 and 5. Possibilities: W V X Z Y or W V Y Z X.
   • Check clue: "Neither K nor J faces Y."
     • Row 1: K is at position 1, J is at position 5.
     • If Row 2 is W V X Z Y: K(1) faces W(1). J(5) faces Y(5). This violates the condition "J does not face Y". Invalid.
     • If Row 2 is W V Y Z X: K(1) faces W(1). J(5) faces X(5). Neither K nor J faces Y. This is valid.

   The final arrangement is:

   W	V	Y	Z	X
   K	L	M	N	J

   
   

   (Row 2 facing North above, Row 1 facing South below)

Analyzing the Statements

Based on the final arrangement (Row 1 South: K L M N J; Row 2 North: W V Y Z X):

• Statement 1: M faces one of the immediate neighbors of X
  • M (Row 1, Pos 3) faces Y (Row 2, Pos 3).
  • X (Row 2, Pos 5) has only one immediate neighbor, Z (Row 2, Pos 4).
  • Does M face Z? No, M faces Y. Is Y a neighbor of X? No.

  Therefore, Statement 1 is False.

• Statement 2: K is one of the immediate neighbors of M
  • K is at Row 1, Pos 1.
  • M is at Row 1, Pos 3.
  • The immediate neighbors of M (Pos 3) are L (Pos 2) and N (Pos 4).
  • K is not L or N.

  Therefore, Statement 2 is False.

• Statement 4: L sits to the immediate right of M
  • L is at Row 1, Pos 2.
  • M is at Row 1, Pos 3.
  • Since M faces South, M's right is towards the direction of lower seat numbers (Pos 2).
  • L is indeed at Pos 2, which is the immediate right of M.

  Therefore, Statement 4 is True.

Since Statement 4 is true, Statement 5 ("All of the given statements are true") is false. Statement 3 ("None of the given statement is true") is also false because Statement 4 is true.

Conclusion

The only true statement regarding M is that L sits to the immediate right of M.