From the University of Cincinnati Professor Stein Carter:

Amino acids are just great
When sitting on your plate.
Your body needs all twenty kinds
To build your bones and minds.
But there are eight that we can’t make:
Essential ones to take
Within your food so you’ll be set,
But some are hard to get.
Three limit others’ usefulness
If you consume much less.
Combine these foods to get them all
So you’ll grow big and tall:
Whole grain with milk or grain with bean
Or peas with seeds between
Or maybe try all three or four
If you want something more.

You must of course hear the accompanying music to appreciate this musical mystery. Don’t quit your day job, Professor Carter!

Here’s the science bit: an explanation of dietary protein requirements at the same website..

Our bodies use amino acids in a specific ratio to each other, so if a person doesn’t get enough of one of them to match with the rest, the rest can only be used at a level to balance with that low one. Most of these amino acids are fairly easy to get in a reasonably well-balanced diet. However, there are three that are a little harder to get than the rest, thus it is important to make sure you’re getting enough of these three. These three are called limiting amino acids, because if a person’s diet is deficient in one of them, this will limit the usefulness of the others, even if those others are present in otherwise large enough quantities. The three limiting amino acids include the sulfur-containing ones (methionine and cysteine), tryptophan, and lysine.

…

Because of publicity from certain agricultural industries, many people in our culture have been taught to think that it is necessary to eat meat to get protein, but this is not true! People in many other cultures do not eat meat yet do get enough protein in their diets. It is true that there are areas of the world where people need to raise cattle and eat meat to survive. For example, in certain arid areas of Africa where almost nothing grows, cattle can graze on the meager grass that’s there that people can’t eat, and the people can eat the milk and meat from those cattle. In our country, the climate is much better, and we can raise many varieties of edible plants, thus we have available alternate (and often better) sources of protein. Some plant protein sources, like soybeans, have a better amino acid balance for humans than meat.

Well, I never.