18a. Leaves broadly triangular (3-7 dm. high; flowers white)
=Buckwheat, Fagopyrum esculentum.=

18b. Leaves from linear to ovate or oblong --19.

19a. Sepals 4; flowers in very long and slender spike-like racemes (4-10
dm. high) =Knotweed, Polygonum virginianum.=

19b. Sepals 5; flowers in spikes or racemes --20.

20a. Flowers on slender pedicels, forming a loose raceme; leaves
linear, jointed at the base (1-3 dm. high; flowers pink or
white; chiefly near the Great Lakes)
=Jointweed, Polygonella articulata.=

20b. Flowers sessile or nearly so, forming a spike or spike-like
raceme --21.

21a. Stipular sheaths at the base of the leaves ciliate at their upper
margin --22.

21b. Stipular sheaths not ciliate at the upper margin --28.

22a. Sheaths with spreading borders --23.

22b. Sheaths without a spreading border, appressed to the stem
(Smartweed) --24.

23a. Leaves ovate, acuminate; stem erect (1-2 m. high; flowers pink)
=Prince's Feather, Polygonum orientate.=

23b. Leaves oblong, obtuse or subacute; spreading or ascending plant of
wet soil =Water Smartweed, Polygonum amphibium var. hartwrightii.=

24a. Peduncles with glandular hairs (5-15 dm. high)
=Smartweed, Polygonum careyi.=

24b. Peduncles not glandular (1-8 dm. high) (Smartweed) --25.

25a. Sepals beset with minute black dots --26.

25b. Sepals white, pink, or red, not black-dotted --27.

26a. Racemes drooping or nodding at the tip; achene dull-colored
=Smartweed, Polygonum hydropiper.=

26b. Racemes erect; achene smooth and shining
=Smartweed, Polygonum acre.=

27a. Sheaths smooth; leaves usually with a dark spot near the base
=Smartweed, Polygonum persicaria.=

27b. Sheaths hairy; leaves not dark-spotted
=Smartweed, Polygonum hydropiperoides.=

28a. Leaves obtuse or somewhat acute at the apex --29.

28b. Leaves acuminate at the apex (5-15 dm. high; flowers white to
pink) (Smartweed) --30.

29a. Stem unbranched, erect, bearing a single terminal raceme (5-30 cm.
high; flowers pink)