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MathNet 2024-part-04 — 168 problems (EN–VI) Question 24

Math Olympiad Vault · MathNet 2024-part-04 — 168 problems (EN–VI)

Question 24

Floor's class consists of $16$ students, including Floor. All students took a test with four questions. Every question was worth a (positive) integer number of points. Each question was marked completely right or completely wrong; no partial points were given. The question that was worth the most points was worth exactly $4$ points more than the question worth the least points. All students achieved a different score; Floor herself got everything right.
At least how many points did Floor score?