# Thread: hard problem

1. ## hard problem

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?

thanks

2. 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?
7. If the other three teachers give you 3rd, you will have 24 points. The most another student can get is 20

What is the smallest number of first-place votes a student could receive and still win the Student of the Year?
0 can get you a 3-way tie, one is required for outright win