# Solution to Nutrition Facts

#### by Evan Chen

We are presented with a pie chart with eight foods, together with a nutrition label, representing a 2000 Calorie diet.

The first step is to complete the nutrition label by filling in the needed percent daily values as defined by the FDA. For posterity, the recommended daily values used in this puzzle are:

• 78 grams fat
• 20 grams saturated fat
• 300 mg cholesterol
• 2300 mg sodium
• 275 grams carbohydrates
• 28 grams dietary fiber

The percentage for protein is never used in the puzzle because, for whatever reason, the percentage for protein is often omitted.

Computing the percentages gives the following label, which has values 8%, 5%, 18%, 18%, 9%, 14%, 7%. Converting to letters, with A=1, B=2, ..., we get HERRING which corresponds to the first of the foods. The label is given below (click to enlarge).

What about the 213.88 number? It turns out this number is redundant, because, given the nutrition facts of a food, it is possible to compute the number of Calories using the 4-4-9 rule: 9 Calories per gram of fat, 4 Calories per carbohydrate and 4 Calories per protein. For example, for this label, we have 213.88 = 9(6.24) + 4(24.75) + 4(14.68).

This gives us a path forwards. The remaining foods in the puzzle are all seven letters (and sorted alphabetically), and therefore for each food we can recover the entire label by plugging in the letters for the percentages — except for the amount of protein. But because the total Calorie counts are given, we can calculate the value (number of grams) for protein too. It turns out that the protein amounts are all integers, so we can extract letters from them.

Working through this procedure gives the following table:

FoodFrom fat and carbsTotal CaloriesFrom proteinProtein (g)
KETCHUP165.22193.22287G
LASAGNA161.24221.246015O
NOODLES230.28290.286015O
PICKLES224.32260.32164D
PUMPKIN233.32257.32246F
RAVIOLI291.36295.3641A
SEAWEED188.38268.388020T

This gives us the final answer, GOOD FAT.