Some nutrition experts contend that potatoes are nutritionally on par with white flour and can be classified as a carbohydrate. If potatoes are eaten with the skin, you are ingesting about every vitamin and mineral necessary for survival.
Eating only potatoes would meet our caloric, protein and fiber requirements. As for the other 20 essential vitamins and minerals, an exclusively potatoes diet meets or exceeds the daily requirements for vitamins B-5, B-6 and C, copper, iron, magnesium, manganese, niacin, phosphorus, potassium, thiamin and folate. However, such a diet would leave us deficient in vitamins A, B-12, D and E, as well as calcium, riboflavin, selenium and zinc, but if the potato is served with either butter or milk, most of those are fulfilled.
While nutritionists wouldn't recommend this, it is technically possible to survive on a potatoes and butter only diet.