The mean of 9 different test scores ranging from 0 to 100 is 85. The median is 80. All test scores are whole numbers. Determine the greatest possible range between the highest and lowest possible test scores.

Let $a$ be the average of all but the median test score, so $a$ is the average of the 8 lowest test scores.

We have $8a + 80 = 9(85)$, so $a = 65$.

The greatest possible range between the highest and lowest possible test scores is $100 - (65 - 1) = \boxed{36}$.