Every year three students are nominated to be “Student of the Year.” After a review process, 10 teachers must rank each student first, second or third place (no ties), with each first-place vote worth three points, each second-place vote worth two points, and each third-place vote worth one point.

Under these conditions, what is the smallest number of first-place votes that it would take to ensure that a student would win the Student of the Year? What is the smallest number of first-place votes a student could receive and still win the Student of the Year?

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