I have a list of chemicals with percentages composing a certain alloy. I am trying to find a way to see all possible combinations summing to 100%, but am a bit stuck with the maths.
For this example, let's consider only a few:
Titanium: 30% to 98%
Iron: 0% to 15%
Niobium: 0% to 40%
How could I see all the possible combinations of these three elements that sum to 100%?
I started down the path by simply finding the product by increments of 1%. But this gives values both less than and greater than 100%.
Thanks, Kris
$$15+40=55; 100-55=45$$
These facts, show that no mixture of these 3 in these ranges hits 100% before titanium is 45%. Any higher, and we have metals sharing percentages without bringing the other two down.
$$100-98=2$$
Shows that even with 98% titanium, you'll need 2% of the other metals. This upper and lower bounds them. It can be thought of in terms of pigeonhole principle.
Similarly anything below 70% Titanium will have to have at least 16% Niobium (rounding up) as that's forced even if you allow an equal as possible mixture of the other two metals. etc.