One total, four possible sets
Take the addresses 1, 2, 3, 4, 5 and 6 and a target sum of 7. Leave the counted-address number unspecified. There are four sets, including a three-address set:
Adding a count of 2 would remove {1, 2, 4}. That is helpful only if 2 is justified. A guessed count can remove the correct explanation before you even see it.
Narrow the possibilities with another clue
Suppose independent information excludes address 1. The sets {1, 6} and {1, 2, 4} disappear. You now have {2, 5} and {3, 4}. If another supported constraint requires address 2, only {2, 5} survives.
When the two sets remain, an investigation that distinguishes address 2 from address 3 is useful. Rechecking the addition is not: both sums already work.
Enter your own case into the calculator
- Enter every relevant printed address. Keep required addresses in this complete list. Do not replace addresses with investigation order.
- Enter the reported total. The numeric tool accepts non-negative whole numbers; a zero total can correspond to an empty set under a compatible model.
- Add required and excluded addresses. Only add constraints supported by the clue model you are testing.
- Leave the count blank unless you know it. It is the number of addresses counted by this clue, not automatically the evil faction headcount.
- Wait for a complete result. A partial or stopped search cannot establish that a set is unique.
Open the Mathematician address calculator and use its example button to load the same 1–6, total-7 case shown here.
Read the result without overclaiming
No sets: one or more inputs do not fit together. Check typos, omitted addresses, an unsupported count and the reliability of the announcement. Several sets: the sum alone has not identified the counted addresses; look for a separating clue. One set: the arithmetic is unique under the current inputs, while the inputs still need to be true.
If the sum looks wrong, inspect the rule
First check whether the displayed Mathematician could actually be a lying Drunkard or another unreliable source. Then check what the role counts. Fall Guy’s Demo rule makes other roles treat it as an evil Underling, so a good Meddler can contribute an address to a clue’s evil set. One recent player mismatch was resolved that way; it is a check to make, not the explanation for every mismatch.
Changes in alignment and timed effects are further reasons to preserve when a statement was obtained. The calculator does not discover those effects. It gives the consequences of the assumptions you explicitly enter.