Read the numbers as addresses
If the counted addresses were 2, 5 and 9, the announcement would be 16 under that model. “16” would not mean sixteen residents. Likewise, a total of 7 does not tell you whether the counted set has two or three addresses.
The true role belongs to the Innocent category and is normally good. The role shown on an investigated card need not be the actual identity: another role can appear as a Mathematician. Decide whether this source is giving normal information before using its number as a firm constraint.
A clue’s evil set can have a special member
Fall Guy’s Demo rule makes other roles treat it as an evil Underling, even though Fall Guy is normally a good Meddler. That can make its address relevant to this sum without making it a normal evil arrest target.
For example, if the real evil addresses in an illustrative case were 3 and 8 and a known Fall Guy were at 1, a clue that includes that special role would count 1 + 3 + 8 = 12. The arithmetic explanation depends on that role actually being present at that address. Do not add an imaginary Fall Guy to make a mismatch disappear.
What to do with the total
Enter your complete address list and total into the calculator. Leave the count unspecified unless you know the number of addresses this clue counts. Add an independent required or excluded address, then look for the clue that separates the surviving sets.
If no set fits, recheck the input model and speaker before making an arrest. If one set fits, its uniqueness is still conditional on your inputs. The worked sum guide walks through the exact four-set and two-filter example.