A group of students are standing in a circle. Each student faces someone across the circle. If student 2 faces student 9, how many students are in circle?
Draw a diagram with a circle, pencil in students 2 and 9 facing each other.
Doesn't this make student 1 faces student 8?
Whom does Student 7 face?
To determine the number of students in the circle, we need to analyze the given information carefully. We know that there are students standing in a circle, and each student faces someone across the circle.
If student 2 faces student 9, it implies that there are seven students between them in the clockwise direction. This is because when we move clockwise from student 2, we count the number of students until we reach student 9.
Now, let's think about the distance between any two consecutive students in the circle. Since the students are standing in a circle, the distance between any two consecutive students would be equal.
In this case, the distance between student 2 and student 9 is 7 students clockwise, which represents exactly one-half of the total number of students in the circle.
To find the total number of students, we multiply the distance between student 2 and student 9 by 2: 7 x 2 = 14.
Therefore, there are 14 students in the circle.