I found several simple (four to seven total foods) diets that, with carefully specified amounts of each food, appear, at face value, to provide full, proper nutrition. Here are a few, with amounts given per day.

• fish/olive/etc
  • 450 g cooked tilapia
  • 450 g ripe olives (yes, that's a lot)
  • 200 g romaine lettuce
  • 200 g cooked lentils
  • 400 g whole-wheat bread (roughly 13 slices)
  • 100 g sweet yellow pepper (half a pepper to one pepper)
• tuna/kale/etc
  • 300 g canned solid-white tuna
  • 150 g walnuts
  • 400 g kale (yes, that's a lot)
  • 700 g boiled pinto beans
• chicken/kale/etc
  • 200 g chicken drumstick (roughly two drumsticks)
  • 100 g mozzarella cheese
  • 300 g flaxseed
  • 300 g kale
• salmon/broccoli/etc
  • 400 g cooked salmon
  • 30 g cheddar cheese (small amount)
  • 200 g almonds (yes, that's a lot)
  • 300 g broccoli
  • 100 g carrots
  • 600 g boiled pinto beans

Each of these is probably deficient in some small (but crucial) ways. Check for yourself before committing to one.

Under stricter circumstances that demand calculated laziness, I might actually follow one of these diets. In practice, I ignore the details and eat with more variety. My diet — as I strive, at least — is based on a food-group heuristic averaged from these specifics of "nerdtrition" (nerd nutrition):

• 300 g to 400 g of animal products (ideally fish, second-best dairy)
• 150 g to 500 g of fatty plants (nuts, avocados, olives, etc)
• 400 g to 700 g of starchy plants (whole-wheat bread, beans, and potatoes being some better ones)
• 200 g to 400 g of nutritionally-complex vegetables (kale, broccoli, spinach, etc)
• 0 g to 200 g of fruit (sweet peppers being one of the better ones)

All else, I see as superfluous, including, especially, processed foods.

Methods

1. Compile a list of nutrients to keep track of.
   • macronutrients
     • water
     • saturated fat
     • unsaturated fat
     • total carbohydrates
     • sugars
     • fibre
     • protein
     • cholesterol
   • minerals — here, only those with common deficiency diseases
     • magnesium (Mg)
     • potassium (K)
     • calcium (Ca)
     • iron (Fe)
     • zinc (Zn)
   • vitamins — likewise, only common deficiencies
     • A (retinol/carotenoid)
     • B6 (pyridoxines)
     • B9 (folate)
     • B12 (cobalamin)
     • C (ascorbic acid)
     • D (calciferols)
2. Determine a minimum (RDA) and maximum (UL) for each nutrient. I mostly got these from conventional sources, like the NIH Office of Dietary Supplements, and adjusted a few of them based on more recent and niche findings:
   • favour more fat over carbs
   • avoid sugar, seriously
   • get enough fibre, seriously
   • there may have been others
3. Compile a list of plausibly-nutritious foods. I thought of 54.
4. Look up the amount of each nutrient in each food, as with USDA FoodData Central.
5. Comparative-advantage, eyeball, and gradient-descend your way to a few-item diet.
   1. Look for nutrients best provided by few specific foods, e.g. vitamin D in fish, or vitamin A in carrots.
   2. Start a list of a couple foods providing some of those distinctive nutrients.
   3. Add other foods dense in specific nutrients, and adjust amounts (with the help of a spreadsheet), to address deficiencies and excesses.

Caveats

The whole process to come up with these diets — and the claim that any one of them suffices — relied on several assumptions, each of which could be wrong:

1. every nutrient with any real risk of deficiency is accounted for in the list used
2. minima and maxima used of nutrients are accurate
3. nutrition data is correct about which foods contain how much of which nutrients
4. versions of foods you get in real life have roughly the same composition as versions measured by the source of nutrition data
5. you can properly and reliably absorb nutrients from all relevant foods
6. you will follow the diet precisely, to within the tolerance for which it suffices
7. adding up macro- and micronutrients actually suffices as the logical basis of a healthy diet

In particular, assumption 1 is wrong in the case of iodine. All diets given here expect iodine supplements, which you'd usually get in practice as iodised salt. Some of the diets (except the ones using salmon) also expect vitamin D supplements.

These caveats may make nutrition seem worryingly fragile. Most people eat healthily-enough with much less worry by accepting a wider variety than seven foods. Nerdtrition was an exercise in minimalism, which taught me a bunch about nutrition in the process.