Group Shares K of Its N Suspects with Another
The first group has exactly N Suspects (or Innocents) in total, and exactly K of those N are cells that also belong to the second group. This encodes two simultaneous constraints: (1) an exact count for the first group, and (2) an exact count for the intersection of the two groups. The remaining N − K Suspects from the first group must lie outside the intersection, which constrains the cells belonging only to the first group. Reason from both the total count and the intersection count together — neither alone is sufficient.
Reading the examples
“Y's neighbors have N suspects, K of which are also in Z's neighbors”
The clue says Alice's neighbors has 1 suspect, 0 of which are also in Eve's neighbors. Given the revealed cells, this overlap constraint forces Bob (Innocent), Diana (Innocent).
“Y's neighbors have N suspects, K of which are also in column B”
The clue says Alice's neighbors has 1 suspect, 0 of which are also in column B. Given the revealed cells, this overlap constraint forces Bob (Innocent), Diana (Suspect), Eve (Innocent).
“Row 1 has N suspects, K of which are also in Y's neighbors”
The clue says row 1 has 3 suspects, 3 of which are also in Eve's neighbors. Given the revealed cells, this overlap constraint forces Alice (Suspect), Bob (Suspect), Carol (Suspect).
“Column A has N suspects, K of which are also in Y's neighbors”
The clue says column A has 3 suspects, 3 of which are also in Eve's neighbors. Given the revealed cells, this overlap constraint forces Alice (Suspect), Diana (Suspect), Grace (Suspect).
“Y's neighbors have N suspects, K of which are also in the edge”
The clue says Eve's neighbors has 2 suspects, 2 of which are also in the edge. Given the revealed cells, this overlap constraint forces Grace (Innocent), Henry (Innocent), Iris (Innocent).
“The edge has N suspects, K of which are also in Y's neighbors”
The clue says the edge has 1 suspect, 0 of which are also in Alice's neighbors. Given the revealed cells, this overlap constraint forces Bob (Innocent), Diana (Innocent).
“Y's neighbors have N suspects, K of which are also in row 1”
The clue says Alice's neighbors has 1 suspect, 1 of which is also in row 1. Given the revealed cells, this overlap constraint forces Bob (Suspect), Diana (Innocent), Eve (Innocent).
“To the left of Y has N suspects, K of which are also in Z's neighbors”
The clue says to the left of Frank has 1 suspect, 0 of which are also in Eve's neighbors. Given the revealed cells, this overlap constraint forces Diana (Innocent).
“Y's neighbors have N suspects, K of which are also to the left of Z”
The clue says Alice's neighbors has 1 suspect, 0 of which are also in to the left of Frank. Given the revealed cells, this overlap constraint forces Bob (Suspect), Diana (Innocent), Eve (Innocent).