Circular Arrangement Setup

This problem involves arranging six people, named F, G, H, I, J, and K, in a circle. They are all facing towards the center. We need to figure out their exact positions based on the given clues to answer the question: Who is standing between F and I?

Analyzing Seating Clues

Here are the key pieces of information we have:

• There are 6 people: F, G, H, I, J, K.
• They stand in a circle, facing the center.
• Opposite Pairs: In a circle of 6, people at positions 1 and 4, 2 and 5, and 3 and 6 are opposite each other.
• Clue 1: F and G are adjacent to each other.
• Clue 2: F and K are opposite to each other.
• Clue 3: H is opposite to I.
• Clue 4: J is opposite to G.
• Clue 5: K is second to the left of H.

Step-by-Step Deduction for Placement

Let's determine the positions step by step:

1. Start with Opposite Pairs: We know the pairs (F, K), (H, I), and (J, G) are opposite each other.
2. Use Clue 5: "K is second to the left of H". Let's assume H is at position 2 (thinking of the circle positions numbered 1 to 6 clockwise). Facing the center, H's immediate left is position 1, and the second position to the left is position 6. Therefore, K must be at position 6.
3. Use Clue 2: "F and K are opposite". Since K is at position 6, F must be at the opposite position, which is 3. So, (F, K) occupy positions (3, 6).
4. Use Clue 3: "H is opposite to I". We placed H at position 2. Therefore, I must be at the opposite position, which is 5. So, (H, I) occupy positions (2, 5).
5. Identify Remaining Pair: The remaining positions are 1 and 4. The remaining pair of opposite people is J and G. So, (J, G) must be either (1, 4) or (4, 1).
6. Use Clue 1: "F and G are adjacent". We know F is at position 3. The positions adjacent to 3 are 2 and 4. Position 2 is occupied by H. Therefore, G must be at position 4.
7. Determine J's Position: Since G is at position 4, and J is opposite G (Clue 4), J must be at position 1. So, (J, G) occupy positions (1, 4).

Derived Arrangement

Based on the deductions, the final arrangement of the people in the circle (moving clockwise) is:

• Position 1: J
• Position 2: H
• Position 3: F
• Position 4: G
• Position 5: I
• Position 6: K

Let's quickly check if all clues hold:

• F(3) and G(4) are adjacent? Yes.
• F(3) and K(6) are opposite? Yes (3 and 6 are opposite).
• H(2) is opposite to I(5)? Yes (2 and 5 are opposite).
• J(1) is opposite to G(4)? Yes (1 and 4 are opposite).
• K(6) is second to the left of H(2)? Yes (H at 2, left is 1, second left is 6).
• All clues are satisfied.

Finding Who is Between F and I

Now, let's find who is between F and I in our arrangement:

• F is at position 3.
• I is at position 5.
• The people are arranged as: J(1), H(2), F(3), G(4), I(5), K(6).
• Looking at the positions between F(3) and I(5), we see position 4.
• The person at position 4 is G.
• Therefore, G is standing between F and I.