Setting Up the Seating Arrangement

We have nine persons (C, D, B, A, J, F, G, H, K) sitting in a straight line facing North. We need to find who sits third to the right of H. Let's use the clues provided to determine the exact seating order.

The clues are:

• G sits second to the right of C.
• B sits fourth to the left of G.
• D is neither an immediate neighbour of K nor B.
• F sits fourth to the right of C.
• F sits second to the left of K.
• K sits fifth to the right of A.
• Only three people sit between J and A.

Deriving the Seating Order Step-by-Step

Let's combine the clues logically:

1. From "G sits second to the right of C" and "F sits fourth to the right of C", we deduce the relative order C ... G ... F.
2. From "F sits second to the left of K", we know K is two places to the right of F. Combining this with the above, we get the relative sequence C ... G ... F ... K. If C is at position x, then G is at x+2, F is at x+4, and K is at x+6.
3. "K sits fifth to the right of A" means there are 4 people between A and K (A _ _ _ _ K). Since K is at position x+6, A must be at position (x+6) - 5 = x+1. Our sequence now looks like: C (at x), A (at x+1), G (at x+2), _ (at x+3), F (at x+4), _ (at x+5), K (at x+6). This structure fits all these relative positions.
4. "Only three people sit between J and A". A is at position x+1.
   • If J is to the left of A (J _ _ _ A), J would be at (x+1)-4 = x-3. This would place J before C, making the sequence J _ _ _ C A G _ F _ K, which requires at least 10 people. This is not possible.
   • If J is to the right of A (A _ _ _ J), J would be at (x+1)+4 = x+5. The sequence becomes C A G _ F J K. Let's check the people between A (x+1) and J (x+5): They are G (x+2), the person at x+3, and F (x+4). This confirms there are exactly 3 people between A and J.
5. The derived sequence is C, A, G, _, F, J, K. This uses 7 positions. The remaining people are B and H.
6. "B sits fourth to the left of G". G is at position x+2. B must be at position (x+2)-4 = x-2.
7. Now let's fit this into 9 positions. Consider the sequence C A G _ F J K. Let's place K at the far right, position 9.
   • Positions: 1 2 3 4 5 6 7 8 9
   • Sequence C A G _ F J K fits as: _ _ C(3) A(4) G(5) _(6) F(7) J(8) K(9).
   • Now place B. B must be at position G-4 = 5-4 = 1. This fits the first position. Arrangement: B(1) _ C(3) A(4) G(5) _(6) F(7) J(8) K(9).
   • The remaining person is H, and the remaining empty slot is position 2. Arrangement: B H C A G _ F J K.
   • The last empty slot is position 6. The only person left is D. Final arrangement: B H C A G D F J K.
8. Let's verify the final arrangement $B H C A G D F J K$ with all clues, especially Clue 3 ("D is neither an immediate neighbour of K nor B").
   • G (pos 5) is 2nd right of C (pos 3): Correct.
   • B (pos 1) is 4th left of G (pos 5): Correct.
   • F (pos 7) is 4th right of C (pos 3): Correct.
   • F (pos 7) is 2nd left of K (pos 9): Correct.
   • K (pos 9) is 5th right of A (pos 4): Correct.
   • 3 people (G, D, F) between J (pos 8) and A (pos 4): Correct.
   • D (pos 6) neighbors are G (pos 5) and F (pos 7). D is NOT a neighbor of K (pos 9) or B (pos 1): Correct.
   All clues are satisfied.

Final Seating Arrangement

The confirmed seating arrangement from left to right (North-facing) is:

Answering the Question

We need to find who sits third to the right of H.

• Locate H in the arrangement: H is at position 2.
• The person 1st to the right of H is C (at position 3).
• The person 2nd to the right of H is A (at position 4).
• The person 3rd to the right of H is G (at position 5).

Therefore, G sits third to the right of H.