Brodie syndrome is
Brodie syndrome is an abnormality of transverse occlusal relationships and was named after Allan G. Brodie, who was the first author to present the case of a patient with this malocclusion in 1952 . 
Other names can be found in the literature: Brodie bite, exaggerated occlusion, or even scissors bite. The term “syndrome” seems inappropriate as medical records differ among individuals, with no specific occlusal disorder or any other clinical, physiological, biological, or radiological symptoms. It is only an abnormal occlusal condition without precise details regarding the structure causing the malocclusion, the underlying etiology, or the presence of associated symptoms.
This malocclusion is clinically defined by a complete lateral position of the maxillary arch in relation to the mandibular arch. The mandibular arch is totally imbricated inside the maxillary arch. Contact is established between the palatal surfaces of the maxillary teeth and the vestibular surfaces of the mandibular teeth.
Scissors bite: Scissors bite refers to a condition in which a tooth or group of teeth in the mandibular buccal arch are lingual to the lingual cusps of the maxillary teeth.
Orthodontics: Diagnosis and Management of Malocclusion and Dentofacial Deformities THIRD EDITION: Om P. Kharbanda, pdf no 318:
When all the teeth are in scissor bite
Open bite in children
Skeletal Class III condition
Cleft palate with cleft lip