eg: Changing the size, shape, or location of the agitator (compared to other manufacturers models), with the resulting change having the desired 50% beneficial effect?
Soo for my competing product I would have to make a physical change and an algometric (software) one in order to compete?
Presumably I could then patent this combination?
Or, seeing as this simply confirmed the 50% efficiency gain of other designs is it not viewed as a 'new' idea, and therefore un-patentable?
I'll extend that question and ask if making a physical change OR an algorithmic one is sufficient?
The 50% is a bit of a red herring and not really important to the invention here other than to confirm that your solution does indeed overcome the problem.
As for whether “a physical change OR an algorithmic one is sufficient” - It all depends on the nature of the problem and the solution.
In our washing machine scenario simply exchanging one algorithm for another is not sufficient to get you a patent of your own but it may be sufficient (depending on the scope of the claims) to mean you are not infringing my patent.
If you made a physical change which is itself novel and inventive (i.e. your physical change is overcoming some other problem or the same problem but in a different way) then this would be sufficient to get you your own patent.
Lets look at a scenario:
If the invention is to mount the agitator horizontally and no one else has done this before (this is hypothetical because I'm sure this would have been tried before) then the invention is potentially patentable. There are inventive step issues to consider, for example, are you simply realizing some (hypothetical) well known fact that it is more efficient to mount a motor sideways - if so, not patentable. Lets assume the invention here is both novel and inventive (This is a strong assumption and not one to be taken lightly. In reality something this broad, like the singular concept of mounting an agitator horizontally, would rarely be novel and/or inventive. Dealing with hypotheticals and having no prior art to look at makes it very difficult to come up with all the reasons why the invention might be considered obvious [Note: inventive step and obviousness are synonyms in the patent world]).
But if we are saying that it is novel and inventive then the inventor could claim "a computer implemented method for controlling a horizontally mounted agitator with method steps a) ... b) ... and c)....". This covers all algorithms which perform steps a), b) and c). If mounting the agitator horizontally really was a ground breaking invention then a), b) and c) could framed broad enough to cover almost all algorithms. Hopefully you can appreciate that the algorithm here is secondary and not what the monopoly is being granted for (there may be copyright in the code - this is a different issue - but it is not the code which makes the invention novel).
I will try to think of another scenario which explores a more intangible problem/solution.