If you cut out all carbs entirely, you could survive off mayo and water, at least until you get scurvy. It's not far off from a keto fat fast (or a severe type 2 diabetes/morbid obesity intervention diet) if you keep the calorie intake down below 1,000 per day.

I guess mayo and iceberg lettuce might work, if drinking actual water is forbidden. Throw in cauliflower, and you solve the scurvy issue.