The game requires us to determine the sitting order of 7 children. 4 boys - F H I J and 3 girls - R S T. Chairs are arranged in a row from west to east, so chair #1 is the westernmost chair and chair #7 is the easternmost chair:
__ __ __ __ __ __ __ 1. 2. 3. 4. 5. 6. 7
The rules tell us that I sits next to and east of the fourth child, so I must sit in the chair #5.
__ __ __ __ I __ __ 1. 2. 3. 4. 5. 6. 7
S seats east of I and it is impossible for a boy to seat in chair #6 since we cannot have two boys in a row, and it is impossible for two girls to take chairs #6 and #7 because then we have only one girl left to assign to chairs 1-4 and 3 boys resulting in boys sitting next to each other in violation of the rules. Thus we can conclude that two girls must be assigned to chairs 1 through 4 along with 2 boys, and 1 boy and 1 girl must be assigned to chairs 6-7 in the following manner:
B G B G B G B 1 2. 3 4 5 6. 7
Since S is east of I, she must be in chair #6.
B G B G I S B 1. 2. 3. 4 5 6 7
The question asks us if F does not sit to any child that seats next to I, which of the following could be true?
If F does not sit next to any child that sits next to I, it means F does not sit in chairs #3 or #7 and he cannot be in chairs #4 and #6 since we cannot have two boys in a row per the role. This means that the only possible seats left for F is chair #1. Since R sits next to F, we can conclude that R sits in chair #2:
F R B G I S B 1 2 3. 4.5 6 7
Let's look at the answer choices: (A) H sits west of F.
Impossible. F is #1 so no one can sit west of him.
(B) J sits west of I.
Could be. J could sit in chair #3, which would put H in chair #7 and T in chair #4:
F R J T I S H
(C) R sits west of F
Impossible. Again, no one can sit west of F.
(D) T sits west of F.
Impossible. F is #1
(E) T sits west of R
Impossible. R is #2 and the only person west of her is F in chair #1.
Let me know if this makes sense and if you have any further questions.
