The schedule for the air-quality examination is fully determined if which one of the following is true?

Emil-Kunkin June 26, 2023

Hi, I'll try to walk through how I solved. I set this up as multi linear and we know that if 8 is on the second day then 2 is on the first day.

_ _ _ _
2 8 _ _

We then know that 3 must be one if our first two slots, and since it can't be with 2, it must be second, which places 7 and 5

_ 3 _ _
2 8 7 5

We also know that since 4 must also be in the first two,

4 3 _ _
2 8 7 5

This leaves 1 and 6, and since 6 cannot go with 7, it must go last, and 1 goes with 7.