Difference between revisions of "1998 IMO Problems/Problem 2"
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| − | In a competition, there are a contestants and b judges, where b ≥ 3 is an odd | + | In a competition, there are <i>a</i> contestants and <i>b</i> judges, where <i>b</i> ≥ 3 is an odd |
| − | integer. Each judge rates each contestant as either “pass” or “fail”. Suppose k | + | integer. Each judge rates each contestant as either “pass” or “fail”. Suppose <i>k</i> |
| − | is a number such that, for any two judges, their ratings coincide for at most k | + | is a number such that, for any two judges, their ratings coincide for at most <i>k</i> |
| − | contestants. Prove that k/a ≥ (b − 1)/( | + | contestants. Prove that <i>k</i>/<i>a</i> ≥ (<i>b</i> − 1)/(2<i>b</i>). |
Revision as of 21:24, 20 July 2020
In a competition, there are a contestants and b judges, where b ≥ 3 is an odd integer. Each judge rates each contestant as either “pass” or “fail”. Suppose k is a number such that, for any two judges, their ratings coincide for at most k contestants. Prove that k/a ≥ (b − 1)/(2b).
