His favored solution introduces subtlety and complexity. Remember that 20-year old binary search bug in the JDK a few years ago? That is the sort of bug that could be lurking in this solution.

I understand not wanting to waste one slot. A third variable (first, last, count) isn't too bad. But if you really hate that third variable, why not just use first and count variables? You can then compute last from first and count, and the two boundary cases show up as count = 0 and count = capacity.