Concept: A deadlock is a situation where a set of processes are blocked because each process is holding a resource and waiting for another resource acquired by some other process. This makes a cycle. Explanation: When n is even: Even processes(P0, P2, P4...) Requests the even resources(R0, R2,.....) and odd processes (P1, P3,...) requests odd resources(Rn-i, Rn-i-2,.....) Then, the system never going to deadlock When n is odd: Even processes(P0, P2, P4...) Requests the even resources (R0, R2,.....) and odd processes (P1, P3,...) requests also even resources(Rn-i, Rn-i-2,.....) Then, the system may fall into deadlock Option 1: deadlock not possible Here, n=40 is even so, the system will never fall into deadlock Option 2: deadlock possible Here, n= 21, is odd, k=12 processes Requests P0 R0, R2 P1 R20, R18 P2 R2, R4 P3 R18, R16 P4 R4, R6 P5 R16, R14 P6 R6, R8 P7 R14, R12 P8 R8, R10 P9 R12, R10 P10 R10, R12 P11 R10, R8 Deadlock is possible here because a cycle is detected here [ alt="F1 Aniket Ravi 08.07.21 D1" src="//storage.googleapis.com/tb-img/production/21/07/F1_Aniket_Ravi_08.07.21_D1.png" style="width: 315px; height: 138px;"> Option 3: deadlock not possible Here, n=20 is even so, the system will never fall into deadlock Option 4: deadlock not possible n = 41(odd), k = 19 P18 requests R18 and R20 P17 Requests R24 and R22 so, the system will never fall into deadlock because k!=21 if k=21 then deadlock possible P19 requests R22 and R20 P20 Requests R20 and R22