I was on my junior-high chess team! One time, another seventh grader and I entered an eighth-grade tournament. Every player played every other player once (round-robin); a win counted as one point and a draw was 1/2 point. My friend and I got a total of 8 points, while all the 8th-graders got the same number of points (as each other). How many eighth-graders were in the tourney, and why?

I was on my junior-high chess team! One time, another seventh grader and I entered an eighth-grade tournament. Every player played every other player once (round-robin); a win counted as one point and a draw was 1/2 point. My friend and I got a total of 8 points, while all the 8th-graders got the same number of points (as each other). How many eighth-graders were in the tourney, and why?

*Note there are two possible answers

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