The solution provided is correct !

Consider the list of insertions 63, 41, 73, 137 followed by 4 more entries which go into the same bucket, say 18, 34, 66, 130 which go into the 3rd bucket. The insertion of 63 causes the first bucket to be split. Insertion of 41, 73 causes the second bucket split leaving a full second bucket. Inserting 137 into it causes third bucket-split. At this point at least 4 more entries are required. to split the fourth bucket. A minimum of 8 entries are required to cause the 4 splits. b) Since all four buckets would have been split, that particular round comes to an end and the next round begins. So Next = 0 again.