This children's game is as old as the hills. In some species, flowers are grouped into one, large head. In others, including goldenrods and asters, small heads are distributed on branches forming a large, airy pattern of blossoms.
Some composites have all ligulate flowers, including dandelions, wild lettuce, and hawkweed.
It is our good fortune that this time of year, in late summer and fall, is the best to see examples of composites, since they are blooming all over in our ditches and fields, prairies and forests. Roadsides that I've driven along these past few weeks have been drenched in yellow and blue, due mostly to members of the Aster family that are now flowering. Much of the yellow is due to goldenrods, Maximilian's and other sunflowers, golden glow, false sunflower, and Jerusalem artichoke. A lot of the blue and purple is due to various asters, including large-leaved aster, Lindley's aster, smooth aster, and New England aster. We eat lettuce well before it flowers, but sunflower seeds come after flowering and pollination.