Round 1:
Room 1: 1-2-3-4
Room 2: 5-6-7-8
Room 3: 9-10-11-12
Room 4: 13-14-15-16
Round 2:
Room 1: 1-5-9-13
Room 2: 2-6-10-14
Room 3: 3-7-11-15
Room 4: 4-8-12-16
Round 3:
Room 1: 1-6-11-16
Room 2: 2-5-12-15
Room 3: 3-8-9-14
Room 4: 4-7-10-13
Round 4:
Room 1: 1-7-12-14
Room 2: 2-8-11-13
Room 3: 3-5-10-16
Room 4: 4-6-9-15