4.06 Whatever It Takes

At the beginning of the episode House was whisked away by the CIA to treat an ill agent. Eventually House diagnosed him with selenium poisoning from eating too many Brazil nuts and returned to PPTH at the end of the episode.
Back in Princeton, Foreman lead the Housepets. This analysis will cover their patient only.

Initial Symptoms: Woman with seizure
Diagnosis: Heat stroke (Foreman) + thallium poisoning (House)

Contributions by Team
House (2): Diagnosis for thallium poisoning by Brennan
Brennan (0): None (see notes)
Cameron (0): None
Chase (0): None
Cole (0): None
Foreman (2): Diagnosis for heat stroke, realizes patient doesn't have polio
Kutner (0): None
Taub (0): None
Thirteen (0): None
Volakis (0): None

Notes: Should I even bother pointing out that Brennan was in error for poisoning the patient with thallium and faking the positive polio test result? It doesn't matter, because Brennan is gone and hopefully in prison. The Housepets can be forgiven for not considering the possibility that someone in the hospital was poisoning their patient.
House probably realized that the patient only had heat stroke when he accepted her as a patient.

4.05 Mirror, Mirror

Initial Symptoms: Man with respiratory distress
Diagnosis: Environmental dependency syndrome (House) + Eperythrozoon infection (House)

Contributions by Team
House (8): Diagnosis for environmental dependency syndrome, sees livedo reticularis (rash), realizes cold agglutinins are causing rash, tells team to search patient's car to get his history, idea to analyze patient's antibodies to find out where he's been, puts patient on lipopolysaccharide to induce fever, idea to imitate patient to trigger his memories, diagnosis for Eperythrozoon infection
Brennan (0): None
Cameron (0): None
Chase (0): None
Cole (1): Suggests finding out where patient has been to find source of infection
Foreman (1): Points out that patient is mimicking names and symptoms of those around him
Kutner (1): Suggests warming patient with hot tub to draw blood for blood cultures
Taub (0): None
Thirteen (1): Knows to treat patient with clarithromycin
Volakis (1): Suggests patient has infection

Notes: Foreman rejoined the team in this episode.
The condition House calls Giovannini Mirror Syndrome is real, but is one isolated case. Its discoverers called it environmental dependency syndrome. The real case was caused by brain damage, but in this episode it wasn't clear if the patient's illness caused it or if it was pre-existing. I've chosen to believe it was separate from his infection and therefore count it as a separate diagnosis.
It was Brennan's idea to perform an ultrasound on the patient to look for abscesses. What was found was a lump of congealed blood that did not forward the diagnosis, however, so Brennan receives no credit.
I wasn't sure whether to give House a credit for trying to find the patient's travel history by testing his antibodies. The antibodies showed that the patient had been to Ohio, and in the end they found out he was from Ohio so I did give House the credit.
Kutner receives an error for not realizing that the patient had real memories.
Foreman suggested a heart biopsy, but since it gave them no information he doesn't receive credit for it.

4.04 Guardian Angels

Initial Symptoms: Woman with grand mal seizure + hallucinations
Diagnosis: Ergot poisoning (Volakis)

Contributions by Team
House (2): Diagnoses patient's late mother with Parkinson's disease, realizes patient's illness isn't vascular
Brennan (0): None
Cameron (0): None
Chase (1): Sees spleen is enlargened
Cole (1): Sees liver is necrotic
Dobson (3): Realizes patient is having delusions as well as hallucinations, idea to question play along with the patient's delusion to get family history, says blood supply to liver and spleen are being cut off
Foreman (N/A): Not involved in the diagnosis
Kutner (0): None
Taub (0): None
Thirteen (0): None
Volakis (1): Diagnosis for ergotism

Notes: House didn't order anyone to search the patient's home or check her food, so how did Cole know that the patient only ate organic food? He didn't realize the significance of this, so I'm not awarding him points.
House and Dobson thinking alike was a running theme in this episode, so theoretically Dobson's points are House's as well.
House is given credit for his post mortem diagnosis of the patient's mother because eliminating genetic illnesses was part of the diagnostic process.
I'm not sure if the visceral angiogram House ordered would have ruled out vasculitis or not, but since House realized this without the angiogram results anyway he doesn't receive extra credit.
Some viewers felt that House realized the correct diagnosis moments before Volakis did. I didn't see evidence to prove that, so Volakis is given credit and not House.
Dobson was fired at the end of this episode.

4.03 97 Seconds

Initial Symptoms: Man with Spinal Muscular Atrophy (SMA) + fainting
Diagnosis: Strongyloides (threadworms) (House + Thirteen)

Contributions by Team
House (3): Diagnosis for Strongyloides, spots necrosis in cervical lymph node, realizes dog died from eating patient's medication
Brennan (0): None
Cameron (1): Idea for xenodiagnosis
Chase (0): None
Cole (0): None
Desai (0): None
Dobson (0): None
Foreman (N/A): Not involved in the diagnosis
Kutner (2): Suggests patient contracted disease in Thailand, idea to test stool
Taub (1): Realizes patient's kidneys are failing
Thirteen (4): Diagnosis for Strongyloides, says trouble swallowing was caused by SMA, realizes patient's lungs are filling with fluid, knows lung fluid should be bloody if patient has cancer
Twin A (1): Idea to put patient on tilt table
Twin B (0): None
Volakis (0): None

Notes: House had already diagnosed the patient before Thirteen did.
Thirteen received an error for not making sure the patient took his medication, though it's unclear why he didn't.
The candidates were working in two teams throughout the first half of the episode.
It's unclear whose idea it was to test the patient's stool, but I have to give it to someone so I gave it to Kutner. After only two weeks the worms shouldn't have been in the patient's stool, but it's where to start looking for parasites.
Volakis is not getting credit for asking House's former fellows for help!
The twins and Desai were fired at the end of the episode.
In a different hospital, Foreman diagnoses a case of anaplastic large cell lymphoma and saves his patient - for which he is fired, ironically.

4.02 The Right Stuff

House begins this episode with 27 fellowship applicants, which he is narrowing down to two or three over a series of episodes. Starting now I am listing the nine that will be crucial for the following episodes and will cross them off as they are eliminated by House.
Because I don't know if the original Housepets will rejoin the Department of Diagnostic Medicine, I will continue to list them as well. From now on I'll list them all in alphabetical order.

The nine prospective Housepets are:
Travis Brennan (#37), epidemiologist nicknamed Grumpy
Jeffery Cole (#18), geneticist nicknamed Big Love
Jodi Desai (#32), veterinarian
Henry Dobson (#26), not a doctor
Remy Hadley, called Thirteen (#13), internist (her name can be seen on Chase's betting slips in Mirror, Mirror)
Lawrence Kutner (#6/9), rehabilitative and sports medicine specialist
Chris Taub (#39), plastic surgeon
Twins (#15A &15B), pediatric endocrinologists
Amber Volakis (#24), interventional radiologist nicknamed Cutthroat Bitch


Initial Symptoms: Woman with synaesthesia
Diagnoses: Von Hipple-Lindau disease (Chase) + pheochromacytoma (Chase)

Contributions by Team
House (2): Idea to test patient's liver by stressing it, performs auscultatory percussion to detect masses in lungs
Brennan (0): None
Desai (0): None
Cameron (0): None
Chase (2): Diagnosis for Von Hipple-Lindau disease, diagnosis for pheochromacytoma
Cole (0): None
Dobson (0): None
Foreman (N/A): Not in episode
Kutner (2): Realizes patient is having a heart attack, suggests using alcohol to stress liver
Taub (3): Notices elevated red blood count, talks patient out of chapel, idea to examine lungs as part of breast implant surgery
Thirteen (2): Suggests "hormone overproduction" caused atrial flutter, idea to administer oxygen in stress test room for medical records falsification
Twin A (0): None
Twin B (0): None
Volakis (1): Suggests patient has problem with her liver

Notes: At the end of the episode it is revealed that both Chase and Cameron are still at PPTH, Chase as a surgeon and Cameron as an attending in the Emergency department (I'm not sure which is more ridiculous). Foreman is running a diagnostic group in a different hospital.
Pheochromacytomas are associated with some types of Von Hipple-Lindau disease.
House started with 27 fellowship candidate in this episode, which were narrowed down to these nine by the end.
Some have argued that during the surgery House did know the correct diagnoses before Chase revealed them. There's no way to be sure and I myself saw no proof of it, so I'm awarding these diagnoses to Chase.

4.01 Alone

Initial Symptoms: Woman injured in building collapse with fever + fluctuating consciousness
Diagnosis: Serotonin syndrome (House) + delirium tremens (House) + Warfarin/estrogen interaction (House) + antibiotics allergy (Cuddy) + mistaken identity (House)

Contributions by Team
House (7): Diagnosis for serotonin syndrome from MAOI/Demerol interaction, diagnosis for delirium tremens from alcohol withdrawal, sees patient has internal bleeding, notices enlargened uterus, diagnosis for Warfarin/estrogen interaction, spots eosinophilic granuloma, diagnosis for mistaken identity
Chase (N/A): Not in episode
Cameron (N/A): Not in episode
Foreman (N/A): Not in episode

Notes: House was working alone in this episode (hence the title) with no team and only Cuddy and a janitor helping him.
Cuddy realized that the patient had pancreatitis, and made the diagnosis for cephalosporin allergy from the lump House spotted on the patient's arm.