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MathNet 2023-part-03 — 191 problems (EN–VI) Question 90

Math Olympiad Vault · MathNet 2023-part-03 — 191 problems (EN–VI)

Question 90

On an island there are 2023 people standing in single file, each of whom is either a knave or a knight: knights always tell the truth, while knaves always lie. If $i$ is odd, the person in the $i$-th position exclaims: "There are at least $i$ knaves"; if $i$ is even, the person in the $i$-th position exclaims: "There are exactly $i$ knaves". How many knaves are there?