Can you actually meet your vitamin and mineral targets through food?

What questions were we asking?

Our first calculation found food combinations that reached the selected vitamin and mineral targets on omnivore, vegetarian, fortified vegan and omnivorous keto diets. But finding a combination of numbers is easier than finding a diet someone can comfortably shop for, cook and eat.

The unfortified vegan combinations did not meet the targets in our food pool. The other results remain conditional: missing nutrient measurements, borrowed values for similar foods and incomplete safety checks prevent us from calling any menu verified and complete.

That is still a useful result. We can show which foods the calculation leans on, how that translates into actual meals, and which assumptions make an apparent success disappear.

We wanted to know whether food could cover the daily vitamin and mineral recommendations within each diet, without asking someone to eat excessive calories or quantities. Meeting those reference amounts is our calculation target; it does not establish an individually optimal diet. Some combinations worked on paper only after we removed ordinary portion limits: one vegetarian result required about 18 large eggs and 417 g of almonds in a single day. We show the complete combination below.

We calculated for men and women separately, for ages 19–30 and 31–50. Pregnancy, breastfeeding, other ages and medical diets are outside this first experiment, but we'll write for those cases too in a later article series.

We included all 13 vitamins, plus calcium, magnesium, phosphorus, potassium, sodium, chloride, iron, zinc, iodine and selenium. Copper, manganese and choline coverage was checked afterward where data were available. Their recommended amounts were not minimum requirements in the model, but their available upper limits still constrained some of the food combinations we looked at. Molybdenum had no usable food values in these records, so we could not calculate its coverage. It remains a data gap for later work.

There are two different scorecards. Recommended amounts depend on age and sex. Daily Values, or DVs, are the reference amounts used on food labels. All figures are daily. “Adequate” marks an adequate intake; the other rows use recommended dietary allowances. These are average daily intake references over time. Requiring each calculated day to reach them all is a constraint of our experiment, rather than a rule to repeat the same meals. The weekly and monthly discussion below explains that distinction.

Here is every nutrient we optimized for:

The recommendation figures come from the official vitamin tables^[1] and mineral tables^[2]; label figures come from the FDA Daily Value table^[3].

Potassium uses an adequate intake: a planning reference based on more limited evidence. Falling below that number alone does not diagnose deficiency. We ran the recommendation scorecard, the label scorecard and both together. Sodium was different: 2,300 mg was a ceiling. The recommendation-based runs also used its 1,500 mg adequate intake as an experimental planning floor. ^[4], ^[5]

For the combined-scorecard calculation, we required the higher of the age/sex recommendation and DV for each nutrient, except sodium. The recommendation-only and DV-only calculations kept their separate targets. For a man aged 31–50, combining them raises iron from 8 to 18 mg, calcium from 1,000 to 1,300 mg and vitamin D from 15 to 20 micrograms. Vegetarian/vegan iron and the zinc sensitivity are additional adjustments, explained with the calculation method below.

After choosing each food combination, we added up its copper, manganese and choline to see how close it came to their reference amounts. We did not change the foods to fill a shortfall in those three nutrients. Their available upper limits still applied. Molybdenum could not be totaled because its food values were missing:

Which diets did we test?

We tested omnivore diets containing plant and animal foods, vegetarian diets allowing eggs and dairy, vegan diets excluding animal foods entirely, and keto diets. Each had two versions: no fortified foods, or ordinary fortified foods allowed. Keto meant no more than 30 g of carbohydrate minus fiber daily.

We also wanted to compare conventional food with an organic/grass-fed basket, but we did not obtain enough matched composition data to test that question. We have excluded it from the comparison. These results say nothing about whether organic or grass-fed choices make the nutrient targets easier or harder to reach.

There were no supplements, meal replacements or nutrient powders. Iodized salt was allowed only in the versions that permitted fortified foods. Calcium-set tofu was allowed as a traditional food ingredient; UV-exposed mushrooms were treated as food processing.

Our data contained 45 identifiable USDA foods plus an iodized-salt case. Each diet used an ordinary supermarket pool and a broader pool adding foods such as liver, shellfish and UV-exposed mushrooms. Seaweed was excluded. “Broader” describes the foods we made available to the calculation; it does not mean these ingredients are easy to find or customary in every household.

Food values came principally from USDA FoodData Central^[6]. Gaps in biotin, iodine and chloride were explored with explicitly matched foods from the UK composition dataset^[7].

Which foods were available to the calculation?

The target-seeking experiments used 45 USDA food records plus an iodized-salt case. Their exact preparations, original individual portion caps and composition sources are listed once in the food-source appendix at the end of this article. The same table also includes the additional foods used in the regular-diet weeks below. Raised F numbers beside ingredients link to their source rows; the return links in those rows lead back to each diet section.

The supermarket pool supplied the basic foods, including the 90%-lean beef-patty record^F5. The broader pool added beef liver^F7, oysters^F12, mussels^F13, quinoa^F21 and UV-exposed portabella mushrooms^F41. Vegetarian and vegan rules still apply, so liver and shellfish are not available to those diets.

When fortification was allowed, either pool could also use vitamin-D-fortified whole milk^F43, fortified soymilk^F44, fortified instant oats^F45 and iodized salt^F46. The first three are historical generic food records, not verified current retail products. Only the salt's sodium and iodine use an exact current manufacturer label: 590 mg sodium and 68 micrograms iodine per 1.5 g. Its chloride is a UK generic-salt estimate, and other components use the USDA salt record. ^[8]

The model also limits whole groups, so it cannot use every food up to its individual cap simultaneously:

Ounce equivalents are approximate weights; calculations use the gram amounts.

Bread was omitted from the target-seeking food pool rather than assuming that an enriched US flour product was unfortified. It is included in the separately chosen regular-diet weeks. Seaweed was omitted pending better iodine-variability and contaminant information. Those are limitations of this food library and not statements that the foods cannot belong in a good diet.

How did the calculation work?

For each nutrient, the basic calculation was:

Daily credited amount = sum of [food grams × nutrient amount per 100 g ÷ 100].

For example, the selected grilled UV-mushroom record contains 13.1 micrograms vitamin D per 100 g. A 130 g portion contributes 130 × 13.1 ÷ 100 = 17.03 micrograms. Ordinary boiled white mushrooms contain only 0.2 micrograms per 100 g in our selected record: the same 130 g contributes 0.26 micrograms. The type and preparation of the mushrooms therefore matter to the result.

For each diet, the calculation worked out how much of the allowed foods would be needed to reach the nutrient targets without exceeding the limits we could check. We then changed the calorie budget and portion rules to see what made a combination possible. Some runs looked for the lightest food combination; another looked for the fewest calories:

Protein had a reference floor of 56 g for men and 46 g for women. Keto also required total carbohydrate minus fiber to be no more than 30 g. These fixed protein screens do not account for personal body weight or activity. The relaxed run retained a 100 g liver cap and per-entry 5 g salt cap; nutrient upper bounds remained active.

Which upper limits were enforced?

The table below uses the US reference framework. They are ceilings, not targets to pursue. Some apply only to a chemical form or added nutrient, so we did not cap every nutrient at its supplement limit.

These limits and their scopes are documented in the official reference tables linked above and the NIH magnesium guidance^[9].

Our conservative calculation credited only part of spinach’s listed calcium to reflect its lower absorption, as explained in the absorption comparison below. The model used that reduced sum for the upper screen as well as the lower target. We therefore also recalculated undiscounted database calcium for the saved conservative solutions and menu days, and for the successful target-relaxation tests. None exceeded 2,500 mg. That separate check is necessary; an absorption discount alone is not an appropriate way to establish compliance with a total-intake upper limit.

How did missing measurements affect the answer?

We kept three calculation layers separate:

A blank nutrient cell stayed unknown. It contributed no credited amount to the exploratory sum; it was not recorded as a measured zero. If some ingredients had known content and others did not, the reported value was a known subtotal. If a target was wholly unquantified, a USDA-only “success” did not mean that target had been met. This distinction is why the diet comparisons below use the matched-food conservative layer, and why even those results remain conditional.

Excluding the unsupported organic/grass-fed scenario leaves four populations × eight diet scenarios × two pools × three target scorecards × six energy/portion modes × three data layers: 3,456 runs. Of these, 2,544 met their numeric constraints and 912 did not. Those are related calculations, not independent people or a dietary success rate. A separate check recalculated every successful combination; it did not independently prove the optimizer's minimum or every infeasibility conclusion.

What do four weeks of regular meals provide?

Before looking at the target-seeking results, start with four weeks of familiar meals. We chose the meals first, then added up their nutrients. There was no calorie goal, nutrient target, portion cap or attempt to repair the menus afterward. We kept the foods associated with each diet, including eggs and dairy for the vegetarian week and fortified staples where people might buy them.

These are illustrative U.S.-style weeks, not measured average diets. Cereal, sandwiches, pizza, curries, leftovers and snacks all appear in USDA food-survey categories, but the portions and frequencies here are our choices. The same portions are compared with all four age/sex groups; they are not estimates of what men and women typically eat. ^[10]

Calories, fiber and sodium before we look at vitamins

Values are seven-day totals divided by seven. Saturated-fat percentage uses the whole week’s saturated-fat energy divided by its total energy. The sodium comparison is a ceiling, not a minimum to reach.

The keto-style week averages 26.5 g of carbohydrate minus fiber, but days 4, 6 and 7 exceed the earlier 30 g daily cutoff. We left those days in: choosing familiar low-carbohydrate meals did not automatically keep every day within that cutoff.

How do their nutrient totals compare?

The table shows the mean contribution per day, using the conservative accounting described in the calculation method above. An asterisk means at least one food lacks a relevant measurement. That number is a partial sum; if it falls below a reference, the missing food contribution could change the conclusion. The reference amounts themselves are in the first table of this article.

* Partial contribution because some food measurements are missing. NE includes the calculated tryptophan contribution where available; missing tryptophan also earns an asterisk. Biotin, iodine and chloride include the previously described matched-food estimates. No missing values were borrowed for the 50 newly added food records.

Calcium here uses the spinach sensitivity described in the absorption comparison later in this article: spinach’s calcium is credited at 5/27 of its listed amount. This is a comparison assumption, not a measurement of absorbed calcium. Without that discount, the four chemical-content means are 954.7, 1,237.4, 1,172.5 and 727.5 mg/day, respectively. The same below-reference calcium findings remain.

Here are the shortfalls in sums with a value for every ingredient, compared with age/sex recommendations. “None identified” does not clear the nutrients marked with an asterisk above. Calcium still uses the stated spinach sensitivity; vegetarian and vegan iron use the 1.8× recommendation adjustment explained in the absorption assumptions below. Zinc marked † falls short only under our 1.5× plant-diet stress test.

† Vegetarian zinc reaches the unadjusted recommendation; the shortfall appears under the higher experimental plant-diet target. A week below a recommended amount or adequate intake is an intake comparison, not a diagnosis of deficiency.

The choice of scorecard matters. The vegan week’s 1,172 mg calcium and 4,432 mg potassium reach the male recommendations of 1,000 and 3,400 mg, but miss the label DVs of 1,300 and 4,700 mg. Its 25.3 mg iron exceeds the 14.4 mg adjusted male recommendation, while falling below the 32.4 mg adjusted female recommendation. The vegetarian week’s 407.6 mg magnesium reaches the 400 mg recommendation for men aged 19–30, but narrowly misses 420 mg for men aged 31–50.

Against label DVs alone, the complete-record shortfalls are calcium, magnesium, potassium and iron for the omnivore week; calcium, magnesium and potassium for the vegetarian week; calcium and potassium for the vegan week; and B1, calcium, magnesium, potassium and iron for the keto-style week. The combined scorecard adds the vegetarian zinc stress-test shortfall, and the higher adjusted female iron target for the vegetarian and vegan weeks.

There are also unresolved possible gaps. For men aged 31–50 against both scorecards, partial sums fall short for D, E, biotin and chloride in the omnivore week; A, D, E, biotin and chloride in the vegetarian week; A, D, E, K, biotin, chloride, zinc and iodine in the vegan week; and D, E, folate and chloride in the keto-style week. Missing measurements prevent treating these as confirmed shortfalls. Molybdenum cannot be assessed in any week.

Fortification explains some results that might otherwise look surprising. The vegan week supplies a credited 3.76 micrograms of B12 a day from the selected historical fortified soy drink. Incidental B12 traces in plant foods were not counted as reliable sources. A different carton could change that result: check its B12, calcium and vitamin D amounts.

The actual meals and quantities

Every day also includes 240 g (8.47 oz by weight) brewed coffee^F96, with 60 g (2.12 oz) fortified whole milk^F43 for the omnivore and vegetarian weeks, 60 g (2.12 oz) fortified soy drink^F44 for the vegan week, or 30 g (1.06 oz) heavy cream^F86 for the keto-style week. We assumed 2 g (0.071 oz) iodized salt added across the day^F46, on top of sodium already in bread, cheese, sauces and other prepared foods. These additions count in every total. Drinking/cooking water contributes no credited nutrients; supplements and alcohol are outside these examples.

Omnivore — seven days

All quantities are edible food weights, including drained or cooked weights where named. Oats are weighed dry; rice and pasta are weighed cooked. Oils, butter and condiments are included below. The egg record is hard-boiled egg used as a composition estimate for other cooked egg dishes, with cooking fat counted separately.

Vegetarian — seven days

Vegan — seven days

Keto style — seven days

For the vegan diets, bread and tortillas are assumed to use plant-only ingredients and the dark chocolate to be dairy-free. The puffed-rice record is historically fortified, including folic acid, and has no recorded B12. Iodized salt uses the sodium/iodine label amounts described in the food-pool explanation above, with chloride estimated separately. Morton label^[8]

What should we compare with the experimental menus?

These familiar meals provide a starting point for the target-seeking menus that follow. They cover many reference amounts without having been chosen to make every total pass. They can also leave shortfalls, and the foods used to supply one nutrient bring other things with them: the vegetarian week is high in fiber, while the keto-style week is much higher in saturated fat. Sodium exceeds 2,300 mg on several days in every chosen week. Those results stayed in the comparison rather than becoming new rules for selecting the meals.

Keep that distinction in mind as we turn to the experiments. The next sections ask whether the computer can find combinations that reach the targets, and what those combinations require us to eat. Compare their portions and variety with these familiar weeks, as well as their nutrient totals.

A personal comparison would start with the foods and portions you actually repeat, including snacks, drinks, cooking fats, salt and fortified brands. Several days can reveal questions worth checking, but habitual intake is a longer-term average: one authored week cannot tell us how common a gap is or diagnose an individual. ^[11]

For these regular-week examples, the upper-limit checks cover only nutrients and forms we can quantify. Added niacin and added vitamin E are not separated well enough for their form-specific limits; some other food contributions and all molybdenum values are missing. Mercury and other contaminants are outside these inputs.

Where did the calculation find a solution?

At 2,000 calories ±5%, all four age/sex groups had the same found/not-found pattern below. Their food quantities and target amounts were not necessarily identical. These results use ordinary portion caps and the matched-food conservative layer. “Recommendations” includes the diet-specific adjustments, not just the unadjusted amounts in the first table.

“Found” means the numeric model found a combination. “Not found” means no combination met its constraints in this particular food pool. Neither result settles the real-world question while essential data remain incomplete.

We also tested 1,600 and 2,400 calories, each ±5%. For the both-scorecards calculation, every row kept the same found/not-found outcome at all three calorie budgets, in both food pools and all four populations.

Omnivore diet: combinations worked without liver or specialty foods

Both unfortified and fortified-allowed supermarket cases found combinations at all three fixed calorie budgets. The unfortified rounded example below uses salmon, sardines, cod, shrimp, an egg, legumes, vegetables, oats, nuts and seeds; it does not require liver or the broader pool.

The example below combines several seafood types with carefully measured amounts of other foods. That makes this particular output awkward to prepare; it does not show that every food-only omnivore diet needs the same ingredients.

Vegetarian: vitamin D separated the two scorecards

The unfortified supermarket cases failed. With fortification allowed, supermarket combinations met the age/sex recommendation targets at 2,000 calories but still failed the DV and combined targets. Vitamin D's recommendation is 15 micrograms here; its DV is 20 micrograms.

The broader pool supplied UV-exposed mushrooms, and both vegetarian variants found combined-target solutions. In the unfortified rounded example, 130 g of these mushrooms supplies 17.03 micrograms of vitamin D; eggs and dairy contribute additional amounts. The vitamin D result depended on using UV-exposed mushrooms; simply adding more ordinary vegetables would not reproduce that contribution.

Vegan: fortification helped, but the food selection still mattered

Unfortified vegan cases failed in both pools. The broader pool resolved the vitamin D obstacle, but B12 and iodine remained limiting in the tested combination of data and restrictions. No reliable B12 credit was assigned to unfortified plants or fungi, even where a legacy record contained a trace value. This planning rule follows NIH guidance on B12 food sources^[12]

Fortified vegan diet cases still failed in the supermarket pool because of vitamin D, but worked in the broader pool. The rounded example uses fortified soymilk and oats, iodized salt and UV-exposed mushrooms. A larger supermarket pool or different fortified products could change that finding. Missing iodine measurements and excluded seaweed also matter to interpretation of the unfortified result.

Keto: the net-carbohydrate constraint did not prevent a solution

Both keto variants found combinations in both pools at all fixed calorie budgets. The unfortified rounded day contains 29.89 g of carbohydrate minus fiber; the fortified-allowed day contains 29.91 g. These results do not establish ketosis.

The unfortified example uses 250 g cooked soybeans, 200 g cooked spinach, other vegetables, seeds and fish.

Did just one or two nutrients prevent a solution?

Yes, in several of the tested cases. We checked this by rerunning the failed 2,000-calorie, both-scorecards cases while relaxing selected minimum targets. Food eligibility, calorie bounds, portion caps, protein and all upper-limit screens stayed in place.

We tested all seven nonempty combinations of vitamin D, B12 and iodine for each of the 20 failed cases: 140 tests, including 60 successful reduced-target combinations independently recalculated afterward. The pattern below held for all four age/sex groups.

“Smallest” here applies only to the tested D/B12/iodine combinations, not an exhaustive search across all pairs of the 23 nutrients. A successful reduced-target combination meets the remaining tested constraints; it still fails the original set of targets.

How far short were those nutrients?

The table below uses men aged 31–50, both scorecards, 2,000 calories ±5%. The diagnostic calculation minimized the sum of proportional shortfalls while keeping the upper, portion and energy constraints.

For example, the vitamin D gap is 20 − 18.06 = 1.94 micrograms, or 1.94 ÷ 20 × 100 = 9.7% on a fortified vegetarian diet. The broader vegan diet's slightly lower iodine amount reflects a different optimized compromise after the vitamin D gap changed.

What would you actually have to eat?

We attempted seven-day prototypes only after finding promising 2,000-calorie combinations. For each population and diet scenario, we used the combined scorecard and conservative matched-food layer, choosing the supermarket pool if it worked and the broader pool otherwise. Excluding the organic/grass-fed scenario leaves 32 possible menu cases: eight scenarios × four populations. There were 28 completed conditional prototypes; the four unfortified vegan cases had no qualifying combination in either pool and did not proceed.

Here is day one of the unfortified omnivore prototype for men aged 31–50. These are weighed ingredient assemblies, not a recommended meal plan. Cooked and drained weights matter.

The whole day's estimated consumed-food cost is $17.70. The cost comparison below gives the dated U.S. price basket, cooking-yield estimates and two less expensive daily candidates. Meal figures are rounded separately; the daily total uses unrounded costs.

That is approximately 1,929 calories and 1.29 kg of edible food. The calculation gives 134 g protein, 75 g fat, 199 g carbohydrate and 46 g fiber. Its seven-day averages are about 1,919 calories and 1.27 kg of food daily.

The awkward part is visible immediately: four seafood ingredients at dinner, including only 15 g of shrimp. The nutrient totals add up, but buying, preparing and portioning that dinner every week is a different challenge. This example shows why a mathematical match needs a practical review before it becomes a meal plan.

Here is the nutrient accounting for that exact day. Percentages use the combined target for men aged 31–50, not automatically the DV. An asterisk means some ingredient contributions remain unknown or incompletely derived: the figure is the credited subtotal, including any accepted matched-food estimates. A figure above 100% therefore establishes the numeric lower-bound result, not a complete measurement or safety certificate.

Amounts use the units in the target column and are rounded to one decimal place. Coverage percentages are calculated from the unrounded amounts. Vitamin E is only just over its target before rounding; vitamin C, D, calcium, potassium and iodine also have small margins.

The unchanged day also supplies 3.403 mg credited copper and 10.264 mg manganese. Credited choline is 546.13 mg against a 550 mg adequate intake—99.3%, with some contributions unknown.

The same profile's unfortified vegetarian prototype averaged about 1.39 kg of food daily, and its fortified vegan prototype about 1.37 kg. Both used UV-exposed mushrooms. The unfortified keto prototype averaged about 1.12 kg. These are different calculated menus, not a ranking of which diet is healthier or easier.

For comparison, these are the complete day-one ingredient lists for those three prototypes. Amounts are grams; food preparations are those in the food-source appendix. They are computational examples, including awkward 5–10 g ingredients.

† These historical vegetarian/vegan examples use a conventional portabella price proxy for the unverified UV-mushroom product; the vegan example also uses unmatched historical fortified-food compositions. Their displayed costs are assumption-based illustrations, not verified purchasable complete menus. These entries are excluded from the new cost searches. All figures price one day, with preparation yields and price sources in the cost section.

The other examples have their own awkward details. The vegetarian day asks for just 5 g of milk, 5 g of kidney beans and 5 g of orange. The vegan day uses both ordinary and UV-exposed mushrooms, two kinds of oats, and only 1 g each of two oils. The keto day includes 5 g of kale, 5 g of mushrooms and 10 g of sweet potato alongside three fish types.

The seven-day stage added constraints that the initial feasibility search did not: at least 38 g fiber for men or 25 g for women, saturated fat no more than 10% of calories, and at least 20% of calories from fat. Non-keto menus also had a 35% fat ceiling, at least 130 g carbohydrate and 150 g fruit. All menu days required 300 g non-starchy vegetables. To force some daily variation, we also required at least 50 g of one specified food: egg, tofu and yogurt rotated across successive days for non-vegan menus; tofu, lentils and chickpeas rotated for vegan menus.

Foods were selected in 5 g increments, oils in 1 g increments and salt in 0.1 g increments. Rounded solutions were recalculated rather than simply rounding a continuous solution and assuming it still passed. To produce different combinations, each day's search minimized a weighted food-gram total: each food received a reproducible weight between 0.75 and 1.25. The search could stop when the gap between the best combination found and the lowest weighted total still possible was at most 3% of that best-found total. This limited the time spent chasing a slightly lighter combination. That tolerance did not allow a nutrient target to fall 3% short. Nutrient and calorie constraints still had to pass their numerical checks.

Does absorption change the answer?

It changed how we counted nutrients and in some cases changed the food combinations we ended up with. In this experiment, however, the joint stress test below did not change which cases found a numeric solution. Multiplying every plant nutrient by a single “absorption rate” would create false precision.

Vitamin A was already expressed in retinol activity equivalents, which account for different vitamin A activity from retinol and carotenoids. Folate used dietary folate equivalents, which distinguish food folate from folic acid.

Vegetarian and vegan recommendation targets used the supported 1.8-fold iron adjustment.

The exact joint stress-test changes were:

NIH describes the food differences for calcium^[13] and phytate effects on zinc^[14]. The UK dataset lists whole-milk iodine at 20, 31 and 41 micrograms per 100 g in its summer, average and winter entries. Its almond biotin value is 64 micrograms per 100 g, while NIH's biotin food table^[15] lists 1.5 micrograms per quarter-cup of roasted almonds. Those are different foods and serving bases, leaving a composition disagreement to resolve. We tested the low milk value and no credited almond biotin to see whether the result depended on these uncertain contributions. The four changes were applied together; the experiment does not isolate the effect of each one.

For example, a vegetarian woman has a 32.4 mg adjusted iron recommendation and an unchanged 18 mg iron DV, so the combined minimum is max(32.4, 18) = 32.4 mg. In the zinc stress test her combined minimum is max(8 × 1.5, 11) = 12 mg. Those are different calculations with different levels of evidential support.

Niacin equivalents include measured niacin plus tryptophan, an amino acid the body can use to make niacin: niacin in mg + tryptophan in grams × 1,000 ÷ 60. Missing tryptophan is flagged rather than silently treated as fully measured niacin equivalents. Vitamin K uses recorded phylloquinone—the K1 form—as a known contribution. Cooked-food records receive no second cooking-loss deduction.

Food combinations can also help absorption. At a lunch of steak, beans and orange juice, vitamin C from the juice can improve absorption of the meal's nonheme iron. Meat contains both heme and nonheme iron, while beans contain nonheme iron; vitamin C's effect should not be treated as an equal boost to all the iron in the steak. We did not make meal-specific absorption adjustments in these calculations.

What happens if calories or portions are unrestricted?

In some cases, it makes reaching daily dietary goals possible mathematically, but unreasonable as a practical diet.

For the same male profile, the unfortified omnivore supermarket model found a minimum of about 876 calories, spread over 1.51 kg of food. That run minimized calories while meeting selected nutrient constraints; it was not designed to provide enough energy to live on.

The corresponding minimum-energy comparisons are below. These all use men aged 31–50, both scorecards, the matched-food conservative layer and ordinary portion caps. Each result is for one day.

None of these low calorie totals is an adequate-energy recommendation. Notice that the supermarket failures remain even with no energy ceiling: ordinary food caps and available nutrient sources still restrict what can be assembled.

A vegetarian day with about 18 eggs

When we instead minimized food weight and removed ordinary portion caps, the unfortified supermarket vegetarian calculation found a combination that works at about 4,018 calories per day. This is the same male profile and combined target system. The entire day's food is below—about 909 g of cooked egg, equivalent to 18 large eggs, and 417 g of almonds, plus four other ingredients.

Amounts and calories are rounded to one decimal for display. The saved unrounded quantities were used to check the targets.

The eggs supply all 20 micrograms of credited vitamin D in this combination. The selected egg record contains 2.2 micrograms per 100 g, so 909g of eggs supply 20 micrograms. The almonds alone contribute about 2,416 calories. This is a way for the calculation to satisfy its constraints, not a sensible daily prescription.

Two more combinations that strain ordinary portions

These use the same profile, supermarket pool, unfortified foods and relaxed portion rules. Figures describe one whole day.

The calculation was trying to reduce food weight, which can favor calorie-dense foods such as nuts. These initial searches also did not apply the later seven-day menu's fiber and fat-balance rules.

This is why “a solution exists” needs a second question: under which limits? Our ordinary daily caps included 150 g of cooked egg—three large eggs—and 60 g of almonds. These were documented analyst choices informed by food portions, not official maximum servings. Removing them exposed excessive amounts rather than quietly declaring the diet impossible.

Did we ask the computer to design the wrong diet?

Our original search favored the lightest collection of food, which can reward small amounts of many ingredients. For this follow-up we compared that goal with using fewer ingredients. Both searches used the same male profile, combined targets, supermarket foods, 1,900–2,100 calories and the same whole-day food-balance checks. Those checks required at least 38 g fiber, 300 g vegetables, 150 g fruit and 130 g carbohydrate, with fat supplying 20–35% of calories and saturated fat no more than 10%. Both also required at least 25 g of each selected main food, 5 g of an oil and 0.1 g of salt.

Oil and salt are counted separately. The seven main ingredients were salmon, cod, chickpeas, calcium-set tofu, broccoli, sweet potato and banana. The result used more food by weight, but a shorter shopping list. It still depended on the selected food compositions and had not been tested in a kitchen. The original lightest-food result therefore did not establish that a long ingredient list was necessary.

How many food changes away was an ordinary-looking day?

We started with the following illustrative day, rather than rebuilding it from scratch. It is not a record of someone's usual intake.

We allowed the program to change one, two or three ingredient amounts while staying within the calorie, protein, upper-limit and portion screens. It chose the changes that reduced the combined proportional nutrient shortfalls the most.

Here and in the later comparison tables, percentage change means (after − before) ÷ before × 100, using unrounded source amounts. Foods added from zero have no defined percentage increase. Rounded food weights can therefore give a slightly different percentage if recalculated from the displayed numbers.

Reaching every selected lower target required six changed ingredient amounts in this bounded search: add salmon and sardines, remove the rice, add spinach and kale, and add measured salt. These change searches did not impose the follow-up menu's additional whole-day fiber, vegetable and fat-balance checks. The lesson is narrower than “six changes fixes a diet”: a day can be close on vitamin C while still having several unrelated gaps. Sodium's experimental planning floor is also part of this count, not a deficiency diagnosis.

Can we simplify the four-seafood ingredient dinner without losing the nutrient coverage?

We let the program rearrange the original day's foods and minimize its ingredient count, while rechecking calories, portion limits, daily fiber and daily fat balance. It retained 9 main ingredients plus salt. Salmon and cod remained, while sardines and shrimp disappeared from this solution.

Which foods were doing most of the work?

We removed one ingredient at a time from the original omnivore day, without replacing it, and recalculated the nutrient contributions. Then we separately allowed the full supermarket pool to try to replace the missing food.

The contribution and nutrient-change columns describe removing that food from the existing day. “Separate replacement search” reports whether a different whole day was found under the same daily checks. Removing the 15 g shrimp alone left all selected micronutrient lower targets covered, although the whole-day calorie and fat proportions still need their own check. Salmon was harder to replace in this restricted pool. That does not make salmon universally essential: changing the food library or allowing fortification changes the question.

What does fixing one nutrient do to everything else?

Two separate food swaps make this tradeoff visible. In the starting day listed above, replacing 100 g carrot with 100 g raw red pepper raised vitamin C from 63.1 to 184.9 mg, but reduced its vitamin A contribution. For the magnesium comparison, we used the same starting day with 30 g dry oats, 150 g egg and 39 g olive oil instead. Replacing 19 g of that oil with 30 g pumpkin kernels raised magnesium from 376.2 to 553.8 mg with almost unchanged calories. These before-and-after nutrient amounts use the selected USDA records.

Here is the tradeoff in each full day, using the ordinary adult-male targets:

The pepper change moved vitamin C above its target but moved vitamin A below its target. The seed change raised magnesium while worsening an existing vitamin E shortfall. Neither swap was designed to complete the entire nutrient table. Calories stayed within the chosen band; other nutrients and upper limits still need their own checks. A food does not become a complete replacement merely because it supplies the nutrient we were looking for.

If one food covers a nutrient, what else comes with it?

The food brings its calories, fiber and volume and weight along with the nutrient. Sometimes that is an easy fit; sometimes the amount becomes the problem. We used the same food records to calculate how much of a single food would contain a selected target, then counted the energy and fiber in that quantity.

Amounts use unrounded calculations; displayed food weights are approximate. A medium carrot is 61 g in the selected USDA record. Vitamin A, E and zinc use the ordinary adult-male recommendation/DV; potassium uses the higher 4,700 mg DV, rather than the 3,400 mg male adequate intake. The zinc illustration does not apply the higher plant-diet sensitivity.

Carrots are a useful counterexample to an overly broad “food would take too much” argument. About two medium carrots contain the selected vitamin A amount, with only about 3 g fiber. Trying to obtain the potassium DV from those same carrots is a different proposition: almost 1.5 kg, roughly two dozen carrots, before the rest of your food.

Lentils make the fiber tradeoff more pronounced. The quantity containing 11 mg zinc also brings about 68 g fiber—approximately 244% of the 28 g DV and 180% of the 38 g adequate intake used for men in our menu calculations. That is already substantial before counting other foods. Almonds illustrate another constraint: the vitamin E contribution uses about 339 calories, which also have to fit the rest of the day.

Those fiber comparisons are reference points, not harm thresholds. The FDA describes the fiber DV as an amount to reach or exceed on most days. Higher-fiber eating can be beneficial, but a large increase can bring gas or bloating, and tolerance varies. Legumes also contain fermentable carbohydrates that can contribute to gas.

Food content also differs from absorption: phytate in legumes can reduce zinc absorption, so the lentil total is not a measurement of zinc being absorbed by your body.

If you insisted on getting one nutrient entirely from one food every day, these are the quantities you would keep having to accommodate. But nutrients can come from several foods, and those foods can change. The practical question is whether the whole eating pattern fits your appetite, digestion, energy needs and taste preferences.

Does the result survive when you stop weighing everything?

The omnivore prototype with four seafood ingredients at dinner had several narrow margins. We tested 1,000 artificial variations of that day, independently changing each ingredient to between 90% and 110% of its listed amount. Only 115 variations retained every selected lower target; 779 stayed within the calorie band. These are simulated serving changes, not measured failure rates among people following a diet.

Rounding main foods to the nearest 25 g, oil to 5 g and salt to 0.1 g left vitamin C at 88.0 mg against 90 mg. Other modeled lower targets remained covered in that rounded version. This does not mean a small one-day shortfall causes deficiency.

What happens if you replace the planned dinner?

We replaced the four-seafood ingredient dinner and sweet potato with 100 g hard-boiled egg, 300 g cooked brown rice, 200 g cooked broccoli and 5 g olive oil. The replacement day still contained about 1,959 calories, but its nutrient distribution changed.

Vitamin D, B12 and iodine amounts are micrograms; calcium and potassium are milligrams. Means are arithmetic over seven days.

The weekly mean stayed below the selected vitamin D, calcium, potassium and iodine targets even though six days repeated the original combination. B12's weekly mean stayed above its target despite the replacement day's shortfall. Nutrients differ in storage and how intake should be assessed.

Would weekly or monthly targets fit real eating better?

For planning varied meals, we think a weekly view could be more practical than a daily checklist of RDA's. You might eat fish one day, lentils another and something entirely different the following week. A diet plan that asks you to repeat one precisely balanced menu every day is too mechanical to be our actual dinner plan.

There is an important correction to make before criticizing daily allowances: they already describe average intake over time. The National Academies' assessment guidance allows day-to-day variation. Requiring every modeled day to reach every lower target was a rule we chose for this experiment. It was not a requirement to eat the same foods daily. ^[19]

What we dislike is turning those useful reference amounts into a daily pass/fail test that obscures the pattern of eating. A weekly summary—or a longer view for foods you eat less often—could show variety and recurring gaps more clearly, while also being much closer to how people actually choose their dinners. Working within a framework of “recommended weekly allowance” or “recommended monthly allowance” would unfortunately not work equally well for every nutrient. The complication is that the body absorbs, stores, uses and loses different nutrients at different rates.

There is therefore no single nutritional “washout period” that tells us how many days everyone can go without each nutrient. Starting stores, absorption, ongoing use and losses all matter, and are all individual, based on taste, dietary choices, supplementation and the timeframe we're looking at. A complete calculation would also keep track of large individual intakes and applicable upper limits; a satisfactory average can hide an unsuitable concentration on one day.

The next useful experiment would let menus vary across a week while checking both their overall nutrient contributions and the timing rules that each nutrient needs. Extending that to a month would need stronger assumptions about retention and turnover.

How much does allowing fortified foods change?

In the broader food pool, the follow-up unfortified vegan search still found no full-target solution. Allowing the historical fortified foods produced one. That is consistent with the original experiment: reliable B12 sources and the available vitamin D and iodine sources mattered more than simply adding calories.

For a concrete product check, our retained historical soy record and a current Silk carton do not have identical nutrition information. A price quote for the current carton cannot validate the historical nutrient totals. The right next step for a purchasable version is to enter that exact carton's serving size, vitamin D, B12, calcium and other declared nutrients, retain unknowns, and recalculate. ^[23]

Fortification therefore changes feasibility in the tested library, but the current product and the old database entry must remain distinguishable. The two cost-minimized days below avoid those unmatched fortified-food entries.

Can the targets fit inside a normal shopping list?

Fewer ingredients help, but package size is a different problem. For the two cheaper daily meal examples below, we repeated each day seven times solely to work out purchasing quantities. The consumed food was worth about $62.63 for the omnivore week and $78.02 for the keto week. Buying whole modeled purchasing units instead came to approximately $84 and $110, respectively, before tax or delivery.

Consumption costs use the unrounded daily amounts. Each whole-unit shop assumes an empty pantry for that period; the monthly illustration is 30 repeats of the same day. Daily shopping totals should not be multiplied to estimate a week: unused packages carry forward. The difference is food left in packages, not automatically food wasted. Dry beans, oil and salt can carry into another week; fresh-food shelf life and freezing would need a real household plan. Salmon was listed in variable-weight portions, so this checkout calculation assumes 0.75-lb (340.2 g) packs within the listing's 0.7–0.85-lb (317.5 g–385.6 g) range. Actual pack weights change the amount paid and left over. These repeated-day baskets are purchasing illustrations, not varied weekly menus or a verified shelf-life plan.

What did the search find for cheaper daily meals?

The search minimized estimated ingredient cost for men aged 31–50, using both scorecards together, within a pool of 31 priced, unfortified supermarket foods. These two examples use the ordinary omnivore/keto nutrient targets, rather than the vegetarian/vegan iron and zinc adjustments. The search retained the 1,900–2,100-calorie band, ordinary food/group caps and the whole-day food-balance checks described above. For keto, it kept the fiber, vegetable and saturated-fat checks and the 20% minimum from fat. It omitted the fruit and 130 g carbohydrate requirements and the 35% fat ceiling, and capped carbohydrate minus fiber at 30 g. It also limited the day to fourteen main ingredients and required at least 25 g of each selected main food. Food amounts use 5 g increments, oil 1 g and salt 0.1 g.

Prices are U.S. online listings viewed on 24 October 2026, in dollars, from a mixed-retailer basket. Some observations came from older retailer listings and may have changed; price and availability were not verified for a single current cart. Daily cost is the value of food consumed, rather than the cost of buying every package from an empty kitchen. Cooking, draining and peel losses are included through the explicit yield estimates. Labor, fuel, water, tax and delivery are excluded. Product listings used for prices do not replace the experiment's nutrient composition records.

These are the cheapest candidates found within that bounded basket and those rules, with the program's mathematical bounds leaving less than 0.1% room for a cheaper answer inside that pool. They are proposed meal assemblies, not kitchen-tested recipes or the cheapest possible diets in every shop.

Example 1: an omnivore day

The daily cost is $8.95. If the modeled edible yield of the uncertain ingredients were 20% higher or lower, keeping prices and the selected quantities unchanged, the estimate would be about $7.74–$10.75.

Example 2: a keto day

All food weights refer to the edible preparation named: beans, soybeans, fish and vegetables are cooked where stated; tofu and carrots retain their original uncooked/raw records. The listed oil and salt are the day's full counted amounts. Water used for cooking adds no cost here. Meal and daily costs are each rounded from unrounded sums, so printed meal costs can differ from the daily total by a cent.

The daily cost is $11.15. If the modeled edible yield of the uncertain ingredients were 20% higher or lower, keeping prices and the selected quantities unchanged, the estimate would be about $9.68–$13.34. This range tests yield assumptions, not all local price variation. The calculated day contains 29.9 g carbohydrate minus fiber.

The omnivore example still asks for three eggs and substantial legumes; the keto example relies on mature soybeans, avocado and sunflower oil. Those features should be assessed for taste, tolerability and individual fit rather than hidden behind the price. Both reach the selected lower targets in the known-data model; the original composition, product and safety gaps remain. The price basket and preparation-yield assumptions are listed after the food-composition appendix.

What changes if one stubborn gap is supplied separately?

The supermarket vegetarian search had no full food-only solution under these constraints. We then removed only vitamin D's lower requirement from the food calculation and kept the other nutrient, portion, calorie and meal screens. The cost search found a roughly 2,098-calorie food combination at about $4.46 a day, supplying 3.5 micrograms of vitamin D from food.

The example tablet was listed at $7.59 for 100 tablets, or about 7.6 cents each. The manufacturer identifies it as 25 micrograms/1,000 IU per tablet. ^[24]

Can food reproduce the amount used in a clinical study?

Sometimes a study's amount is far outside ordinary food quantities. A three-month randomized migraine trial in 55 participants compared a 400 mg riboflavin dose with placebo. We use the trial here only to define a quantity to translate, without reassessing its treatment effect. Schoenen and colleagues, 1998^[25]. As you can see on the few examples below - theoretically - it can. but reasonably, you can't eat so much. No one can.

We found a difficult menu. Did we prove eating well is difficult?

No. We found combinations that satisfied a particular set of nutrient and food constraints, and some of those combinations were awkward. That is different from showing that every satisfactory diet must be awkward.

The follow-up objective comparison makes the distinction concrete: with the same portion minima and nutrient screens, minimizing ingredient count produced seven main foods where minimizing food weight produced thirteen. Restricting simplification to the original day's ingredients still reduced it to nine main foods plus salt. The priced searches found two further candidates whose quantities could be assembled into named meals.

The defensible conclusion is that our first objective produced some inconvenient answers—and changing the objective can make those answers simpler, on add more questions, or just yield bizarre results

What else separates these calculations from usable diets?

We still cannot confirm that these combinations supply every selected nutrient. That requires more complete food-composition data, current fortified-product labels, and checks on the actual ingredients and portions. Labels help identify products and added nutrients, but they do not report every nutrient, micronutrient and trace element.

Some foods lack measurements for required nutrients. Similar-food estimates do not resolve that uncertainty. Other foods, especially animal protein and vegetables have high variability of micronutrient contents depending on either the animal's diet or the soil the plants grew in, fertilizer use and other similar considerations. Historical fortified-food records also need matching to products sold today: the current Silk unsweetened soymilk label^[23] differs from the generic record used here. These generic records cannot tell an individual that their actual shopping basket meets every target. Averaging more brands would still leave the exact products uncertain. The experiment can reveal limiting nutrients and awkward quantities; turning a proposed combination into a personal meal plan requires checking the foods that person can buy and use.

Taste is another feasibility constraint. A fish-heavy solution may be useless to someone who dislikes fish. Taste, texture, allergies, ethical concerns, cost and access to ingredients all affect which foods someone can eat. We're already planning a much broader series of articles to cover this whole topic.

The bottom line

Food-only combinations reached the selected targets for several diets in this experiment, but the quantities show why meeting nutrient totals is only the first step. Some outputs used tiny portions of many ingredients; others worked only with amounts such as 18 eggs in a day. Vitamin D sources, reliable B12 sources and the exact fortified products made a substantial difference. The follow-up searches found simpler combinations and two priced daily candidates, but matching them to current products and testing them as everyday recipes remains unfinished.

We did not have a particular result in mind when we started. This was a broader version of "Can I get enough of a nutrient on this diet?", and modern AI tools helped us explore the calculations. The answers opened up further questions about food choices, costs and how to turn calculated quantities into practical meals. The additional calculations here begin that work: their strongest finding is that changing what the program optimizes can substantially change the menu it produces.

Food composition data

This single table contains all 96 food entries: 95 distinct USDA records and the hybrid iodized-salt case. USDA numbers identify exact records in its older food-composition database, SR Legacy. They are not checks of today’s shop labels. Enriched and fortified records keep their added nutrients; composite foods such as pizza and pancakes are not counted again as separate flour or cheese.

“Regular weeks” means the four meal examples chosen before nutrient scoring. “Target-seeking” identifies diets in whose successful calculations or rounded prototype menus that food appeared; availability in a pool alone does not count as use. The usage column includes the original age/sex, scorecard, calorie and sensitivity runs and the subsequent menu prototypes, excluding the dropped organic/grass-fed scenario. It does not mean every example of that diet contains the food.

The individual caps below belong to the initial target-seeking model. They did not constrain the regular weeks, and the relaxed-portion experiments removed ordinary caps as described above. All food weights refer to the edible preparation shown. Subscript return links take you back to the relevant regular week or experimental-diet result.

Food quantities are shown in metric and approximate U.S. weight units; oz means weight, while fl oz means U.S. fluid volume. Nutrient amounts retain the mg, microgram and gram units used on U.S. nutrition labels. Small salt amounts still need a suitable scale; the rounded U.S. values do not change the underlying calculation. Unit conversion factors^[26].

Fortified milk, soy drink, cereal and other historical formulations can differ from current products. The iodized-salt row is a separately identified hybrid entry even though it reuses generic USDA salt for residual components. Biotin, iodine and chloride estimates remain subject to the matched-food limits explained in the method; a food-source link does not make missing measurements complete.

What prices and purchase-to-plate assumptions did we use?

The following basket also prices the earlier menu tables. A yield is the edible prepared quantity credited to a package; it is not an additional nutrient absorption factor. Dry beans and lentils use an assumed 2.5-fold cooked mass; rice and quinoa use threefold. Other preparation losses and per-fruit edible sizes are estimates, exposed here so the prices can be changed rather than treated as exact measurements. Fresh/frozen fish fillets use the published 70% cooked-yield factor. ^[27]

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