Problem 352

Solution 1:

The number of students to the left of Pedro, $23$, added to the number of students to
the right of Hwie-Lie, $15$, is $23+15=38$.

In this count, each of the students sitting in between Pedro and
Hwie-Lie is counted twice, while all other students (including Pedro and
Hwie-Lie) are each counted once.

Since the total number of students sitting in the row is $34$, then $38-34=4$ students are counted twice, and
so the number of students seated between Pedro and Hwie-Lie is $4$.

Solution 2:

Suppose that the number of students seated in between Pedro and
Hwie-Lie is $x$.

Not including Hwie-Lie, there are $23-1=22$ students seated to Pedro’s
left.

Since $x$ of these $22$ students are seated in between Pedro
and Hwie-Lie, then $22-x$ are seated
to the left of Hwie-Lie.

Similarly, not including Pedro, there are $15-1=14$ students seated to Hwie-Lie’s
right.

Since $x$ of these $14$ students are seated in between Pedro
and Hwie-Lie, then $14-x$ are seated
to the right of Pedro.

The total number of students seated in the row, $34$, is the number of students seated to
the left of Hwie-Lie, plus the number seated to the right of Pedro, plus
the number seated in between Pedro and Hwie-Lie, plus $2$ (to count Pedro and Hwie-Lie).

Therefore, $34=(22-x)+(14-x)+x+2$ or
$34=38-x$, and so $x=38-34=4$.

The number of students seated between Pedro and Hwie-Lie is $4$.