A syllogism is a logical argument that applies deductive reasoning to arrive at a conclusion (C) based on two (A & B) or more (…N) premises that are asserted or assumed to be true.
Notice here that the premises are assumed to be true, but are not perforce true. It is always a good practice to re-examine one’s premises if one gets stumped in the process of finding a solution to a particular problem. Go back to the basics!
You can have two sets of particulars that can be interpreted in one or more ways, and therefore the outcome may be different to one arrived at earlier.
Get someone who is infinitely intimate with the subject matter to simplify it to its most basic forms. Once you get there, the problem and the solution may be obvious without further research. (eli4)
Always look for analogies in other fields.
Avoid adding apples up to pears and expecting a total number of oranges.
Remember that people hardly ever behave in a logical fashion.