▁to ▁aff irm ▁three ▁things : ▁▁ ▁S 1 : ▁The ▁h anging ▁will ▁occur ▁on ▁Monday ▁or ▁T ues day . ▁ ▁S 2 : ▁If ▁the ▁h anging ▁occurs ▁on ▁Monday , ▁then ▁the ▁prisoner ▁will ▁not ▁know ▁on ▁Sunday ▁evening ▁that ▁it ▁will ▁occur ▁on ▁Monday . ▁ ▁S 3 : ▁If ▁the ▁h anging ▁occurs ▁on ▁T ues day , ▁then ▁the ▁prisoner ▁will ▁not ▁know ▁on ▁Monday ▁evening ▁that ▁it ▁will ▁occur ▁on ▁T ues day . ▁ ▁As ▁a ▁first ▁step , ▁the ▁prisoner ▁reasons ▁that ▁a ▁scenario ▁in ▁which ▁the ▁h anging ▁occurs ▁on ▁T ues day ▁is ▁impossible ▁because ▁it ▁leads ▁to ▁a ▁contradiction : ▁on ▁the ▁one ▁hand , ▁by ▁S 3 , ▁the ▁prisoner ▁would ▁not ▁be ▁able ▁to ▁predict ▁the ▁T ues day ▁h anging ▁on ▁Monday ▁evening ; ▁but ▁on ▁the ▁other ▁hand , ▁by ▁S 1 ▁and ▁process ▁of ▁elim ination , ▁the ▁prisoner ▁would ▁be ▁able ▁to ▁predict ▁the ▁T ues day ▁h anging ▁on ▁Monday ▁evening . ▁ ▁Ch ow ' s ▁analysis ▁points ▁to ▁a ▁subt le ▁f law ▁in ▁the ▁prisoner ' s ▁reasoning . ▁ ▁What ▁is ▁impossible ▁is ▁not ▁a ▁T ues day ▁h anging . ▁ ▁R ather , ▁what ▁is ▁impossible ▁is ▁a ▁situation ▁in ▁which ▁the ▁h anging ▁occurs ▁on ▁T ues day ▁despite ▁the ▁prisoner ▁knowing ▁on ▁Monday ▁evening ▁that ▁the ▁judge ' s ▁assert ions ▁S 1 , ▁S 2 , ▁and ▁S 3 ▁are ▁all ▁true . ▁