{"status": "success", "data": {"description_md": "Six players compete in a chess tournament. Each player plays exactly two games against every other player. In each game, the winning player earns 1 point and the losing player earns 0 points; if the game results in a draw (tie), each player earns $\\frac{1}{2}$ point. What is the minimum possible number of points that a player needs to earn in order to guarantee that he has more points than every other player?\n\n$\\text{(A)}\\ 8\\qquad\\text{(B)}\\ 8\\frac{1}{2}\\qquad\\text{(C)}\\ 9\\qquad\\text{(D)}\\ 9\\frac{1}{2}\\qquad\\text{(E)}\\ 10$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "

Six players compete in a chess tournament. Each player plays exactly two games against every other player. In each game, the winning player earns 1 point and the losing player earns 0 points; if the game results in a draw (tie), each player earns \\frac{1}{2} point. What is the minimum possible number of points that a player needs to earn in order to guarantee that he has more points than every other player?

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\\text{(A)}\\ 8\\qquad\\text{(B)}\\ 8\\frac{1}{2}\\qquad\\text{(C)}\\ 9\\qquad\\text{(D)}\\ 9\\frac{1}{2}\\qquad\\text{(E)}\\ 10

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Cayley, by CEMC, is licensed under the CC BY-NC 3.0 DEED. They are not affiliated with or endorse TopsOJ in any way.

\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2015 Cayley Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/15_cayley_p23", "prev": "/problem/15_cayley_p21"}}