Question

1) A computer class has 28 students, all in their 1st, 2nd, or 3rd year. A)...

1) A computer class has 28 students, all in their 1st, 2nd, or 3rd year.

A) Show that there are at least ten students in the class who are in the same year.

B) How many students would have to be added to the class, at least, to ensure that at least 12 are in the same year?

Homework Answers

Answer #1

A.

Even in the worst case, there have to be 9+9+10.

Since this combination also satisfies the condition of at least ten students in one class, any other combination will also satisfy it.

If any student is replaced from one class to the other, the number of students have to be 10 in at least one class.

B.

There are already 28 students. to ensure that there are at least 12 of the same year, we would need 34 students in the class.

Thus, 6 students would have to be added in the class, to ensure that there are at least 12 in the same class.  

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