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Student #10 is directly across from student #1. In order to evenly pair the sides of the circle, there must be 9 students in each hemicircle, across from the other 9, who will each have a number 9 higher. Student 10 is the first student of the second 9, numbers 10 through 18.

Q: If there are 18 students standing in a perfectly even circle Which student is directly opposite student number 1?

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Long Answer: I found it's actually more difficult to draw these 'students standing evenly spaced in a circle' problems with large numbers of students than it is to just develop a rule for the problem using more simplistic circles (such as a circle with four or eight students). Anyway a general rule for these problems is x+(1/2*t)=y, where x is the number of the particular student (1, in this case), t is the total number of students in the circle (must be an even number, otherwise they can't be standing directly opposite) and y will be the number of the student that the student you have picked is facing. Just a note that, obviously, if you picked student number 18 in this case, this would work out to student number 27. All you have to do in this case is subtract 18 from this number. So student number 18 would be facing student number 9. So if y in the above equation is greater than the total number of students, simply subtract the total number of students from the number you get. Short Answer: 1+(1/2*18)= 1+9 = 10 Student 1 will be facing Student 10.

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