Exactly One Person Has N Suspect Neighbors
Among all cells in the named group, exactly one cell has exactly N Suspects (or Innocents) in its 8-neighborhood. All other cells in the group must have a neighbor count different from N. Neighbors are counted globally across the whole grid, not only within the group. This requires testing each candidate cell: which one can have exactly N Suspect neighbors while every other group member simultaneously has a different count? The constraint is violated as soon as two cells in the group both achieve a neighbor count of N.
Reading the examples
“Only one person in row 1 has exactly N suspect neighbors”
The clue says only one person in row 1 has exactly 1 suspect neighbor. Given the revealed cells, satisfying this uniqueness forces Diana (Innocent), Eve (Suspect), Frank (Innocent).
“Only one person in column A has exactly N suspect neighbors”
The clue says only one person in column A has exactly 1 suspect neighbor. Given the revealed cells, satisfying this uniqueness forces Bob (Innocent), Eve (Suspect), Henry (Innocent).
“Only one person in the edge has exactly N suspect neighbors”
The clue says only one person in the edge has exactly 3 suspect neighbors. Given the revealed cells, satisfying this uniqueness forces Diana (Innocent), Frank (Innocent), Grace (Suspect).
“Only one person in the corners has exactly N suspect neighbors”
The clue says only one person in the corners has exactly 1 suspect neighbor. Given the revealed cells, satisfying this uniqueness forces Henry (Innocent).