# If Frank does not sit next to any child who sits next to Ivan, which one of the following statements could be true?

Tehran20 on October 21, 2019

Why B?

Can I please get this diagrammed?

Irina on October 21, 2019

@Tehran20,

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.