I believe it's 21 because:
+0 stats with 10/10/1 fragments = 80%
+10 stats with 10/10/1 fragments = 40%
So, to go from 40% to 80% you have to use 20 fragment(III) plus the one you would normally use unless the first MR is 80% regardless of how many fragment(III) you use. Either way you are right, should be 20/21.
Would be cool if jamie/someone can confirm so I can update my MR calculator.
These are the one's I've done so far
Wind +19 - 31 Fragment 3 with Master Refiner's Ore - 85%
Wind +24 - 41 Fragment 3 with Master Refiner's Ore - 85%
MC 0 - 1 Fragment 3 without Master Refiner's Ore - 80%
MC +5 - 10 Fragment 3 without Master Refiner's Ore - 80%
MC +10 - 20 Fragment 3 without Master Refiner's Ore - 80%
MC +10 - 23 Fragment 3 with Master Refiner's Ore - 85%