Track / Stage 5 / 10 of 400 #610 of 1964

Problem 610

AIME late

Combinatorics Difficulty 5.0 Find the answer

78. In a chess tournament, there are an odd number of participants, and each participant plays one game against every other participant. A win earns 1 point, a draw earns 0.5 points, and a loss earns 0 points; it is known that two of the participants scored a total of 8 points, and the average score of the others is an integer. How many participants are there in the tournament?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Reference answer: 9

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.