Question

A king has unflinching loyalty from eight of his ministers M1 to M8, but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate at least one of the likings of any of the other three persons selected.
M1 likes fishing and smoking, but hates gambling.
M2 likes smoking and drinking, but hates fishing.
M3 likes gambling, but hates smoking,
M4 likes mountaineering, but hates drinking,
M5 likes drinking, but hates smoking and mountaineering.
M6 likes fishing, but hates smoking and mountaineering.
M7 likes gambling and mountaineering, but hates fishing.
M8 likes smoking and gambling, but hates mountaineering.

• A. M1, M2, M5 and M6
• B. M3, M4, M5 and M6
• C. M4, M5, M6 and M8
• D. M1, M2, M4 and M7

Hint:

Model as graph: nodes = ministers, edges = shared likes; verify hate constraints per edge.

Answer 1

The Correct Option is C

Check shared-liking graph: {M4, M5, M6, M8} form connected set with required hate–like conditions satisfied. Others break rule.