operating syatem

Question

system has 9 identical resources and N processes competing for them..Each process can request at most 4 resources

what is the minimum possible value of n which will lead to a deadlock?

Answer 1

Minimum value of n= 3 as if their are three process and each process requires at most 4 (max 4) instance of resources , so while having 3 process ,suppose each process had acquires 3 (max-1)resouces so, in this case no process can execute and can get 1 resouces and the system will be in deadlock .

Answer 2

only 2 process no possibility of deadlock

3 process deadlok may or may not occur (deadlock  3,3,3 rest combinations are deadlock free) this could be ans if they had asked what is the minimum possible value of n which could lead to a deadlock?

4 process again deadlock may or may not occur (deadlock 3,2,2,2  deadlock free 4,2,2,1 etc )

5 process again deadlock may or may not occur (deadlock free 4,2,1,1,1 )

and so for 6 processes deadlock may or may not occur (deadlock free 4,1,1,1,1,1)  

for 7 process (3,1,1,1,1,1,1) deadlock is must so it will surely lead to deadlock hence ans should be 7

after 7 i.e for 8 ,9 etc deadlock is must so min value is 7