Can you lose weight by eating just fat?

I found a study that was published in the late 50s by a doctor Kekwick. He put 3 groups on different very-low-calorie diets.

Group 1: 1000 cal, 90% fat.
Group 2: 1000 cal, 90% protein
Group 3: 1000 cal, 90% carbs

Now if you have read my previous post on "Big fat carb problem" you may be able to guess which group lost the more fat. Here are the results.

Group 1: -0.9 lbs per day
Group 2: -0.6 lbs per day
And Group 3: drum roll please.... +0.24 lbs per day.

Do you understand why we have a big fat carb problem?