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The sole purpose of hashcode() is to come up with efficient way of finding Hash buckets. Once a bucket is determined the overridden equals method can be used to retrieve that element.

Without hashcode method, all the elements can be inside a single bucket and hence result in inefficient hashes.

1)Assume, the equals method is overridden correctly and hashcode is left to default implementation. Now

EqualsOnlyObject o1 = new EqualsOnlyObject();
    HashSet hs = new HashSet();
    EqualsOnlyObject o2 = o1.clone();  //As per equals, o1 == o2 (but what abt hashcode?)
    hs.Add(o1);  //Added successfully
    hs.Add(o2);  //this too is added successfully(default hashcode is unique, as  its mostly the memory address of the object)
    PRINT hs.Count();  //should print "2"

2)But assume if the hashcode is overridden properly then hs.Add(o2) should not add the object "o2" since they are identical.

To obey rule i.e if two objects are equal,it means their hash codes are equal. Just imagine an object with 3 properties and respective class has equals method definition which considers only 2 proprieties out of 3. then we should implement hashcode() also by using same prosperities.