17a. Leaves narrowly lanceolate or linear-oblong; rare species =Knotweed, Polygonum ramosissimum.= 17b. Leaves broadly oblong, oval, or elliptical; common weed of yards and gardens =Knotweed, Polygonum erectum.= 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) =Bistort, Polygonum viviparum.= 29b. Stem branched, submerged in water or creeping on muddy shores (flowers pink) =Water Smartweed, Polygonum amphibium.=