Testing Strategy

You’re in charge of a school with 1000 students. You know that exactly one student has COVID-19 but you have no idea which one it is.

You have a test kit that will allow you to send in up to 10 vials of saliva to be tested. All the samples must be sent at the same time and you will not get another chance to test the students.

You can combine samples from multiple students into one vial and test the vial as a whole. For example, you could number the students 1-1000 and then put samples from students 1-100 in the first vial, 101-200 in the second vial, etc.

Using this strategy, you could identify a group of 100 students to quarantine and the other 900 could continue to come to school.

Your goal is to be able to quarantine as few students as possible.

Is there a strategy for combining test samples into the 10 vials that will allow you to quarantine fewer than 100 students?

If so, what is that strategy and how many students would you have to quarantine after getting the test results?