Read the details provided below carefully and answer the following question.

A certain number of persons sit in a row facing north. E is the only neighbor of Q. Five persons sit between E and T. K sits immediately to the right of T. B sits second to the right of K. Two persons sit between K and Y. The number of persons sitting between E and H is twice the number of persons sitting between B and Y. The number of persons sitting to the right of Y is four less than the number of persons sitting to the left of Y. More than twelve persons sit in the row.

If H sits second to the right of S, then how many persons sit between S and Q?

The correct answer is Eleven.

Step 1: Understand the positions based on Q being at an extreme end.
Since E is the only neighbor of Q, Q must sit at one of the extreme ends of the row, and E sits immediately next to Q.
Let us analyze the case where Q is at the extreme right end of a row containing $N$ persons facing North (numbered 1 to $N$ from left to right):

• Position of Q = $N$
• Position of E = $N-1$

Step 2: Position T, K, B, and Y relative to E.
Five persons sit between E and T. Moving left from E:
Position of T = $(N-1)-6=N-7$
K sits immediately to the right of T:
Position of K = $(N-7)+1=N-6$
B sits second to the right of K:
Position of B = $(N-6)+2=N-4$
Two persons sit between K and Y. Placing Y to the left of K:
Position of Y = $(N-6)-3=N-9$

Step 3: Determine the total number of persons ($N$).
The number of persons sitting between Y ($N-9$) and B ($N-4$) is:
$(N-4)-(N-9)-1=4$ persons.
The number of persons between E and H is twice the number of persons between B and Y:
Persons between E and H = $2\times 4=8$ persons.
Placing H to the left of E ($N-1$):
Position of H = $(N-1)-9=N-10$.
Now, determine the number of persons to the left and right of Y ($N-9$):

• Persons to the left of Y = $N-10$
• Persons to the right of Y = $N-(N-9)=9$

Step 4: Determine the positions for $N=23$.
Substituting $N=23$ into our derived positions gives:

• Position of Q = 23
• Position of E = 22
• Position of T = 16
• Position of K = 17
• Position of B = 19
• Position of Y = 14
• Position of H = 13

Step 5: Find the position of S and calculate the number of persons between S and Q.
H sits second to the right of S, which means the position of H is 2 positions to the right of S:
$13=\text{Position of S}+2\Rightarrow \text{Position of S}=11$
The number of persons sitting between S (position 11) and Q (position 23) is:
$23-11-1=11$
Therefore, exactly 11 persons sit between S and Q.