Rank inflation and maths

TrT has long argued that rank inflation has a simple, if somewhat brutal, solution.

Brigadier Generals Command Brigades.
If there is not a Brigade sat under you, you cannont be a Brigadier

If we cut out some of the ranks (to make my life easier) we get

Which means our army of 82000 or there abouts, needs twenty brigadiers (and twenty Brigades),

The Reality (H/T Think Defence), is that the combined services have THREE HUNDRED AND FORTY, even if we assume the army has only one third of them, is is over manned 6:1

Excel is the answer to all questions