Suppose students in your school arrive in groups each morning. You are the first to arrive, and you are alone, but still considered a group (consisiting of one person). The second group has two more people than the first group. The third group has two more people than the second group. If 576 students come to school in this day, how many groups arrived at school, assuming they all meet the requirment of having two more members than the group before them?

Question

Suppose students in your school arrive in groups each morning. You are the first to arrive, and you are alone, but still considered a group (consisiting of one person). The second group has two more people than the first group. The third group has two more people than the second group. If 576 students come to school in this day, how many groups arrived at school, assuming they all meet the requirment of having two more members than the group before them?
I could write it out the long way, but can someone show me a short cut, or pattern?
Thanks!

tchrwill · Answer

Based on your numerical definition of the groups, the groups are 1-3-5-7-9-11-3-13-15-etc.

The sum of any group of "n" odd numbers starting with 1 is n^2.

Since 576 students arrived at the school, the number of groups must be sqrt(576) = 24.