The hero is told to go and kill the thing that cannot be killed. In Apollodorus's Library (a Greek mythography compiled in the 1st–2nd century CE), Hercules is set his labours, and the first is to "bring the skin of the Nemean / lion" — "an invulnerable beast begotten / by Typhon". Arrows glance off it, so he corners the lion in a two-mouthed cave, blocks one entrance, comes in through the other, and kills it with his bare arms: "putting his arm round its neck" he holds it until he has "choked it". The next command only raises the stakes — Eurystheus "ordered him to kill the / Lernaean hydra", the many-headed swamp-creature that grows two heads for each one severed.

The same ordeal shapes the fourteenth canto of the Kalevala (compiled from Finnish oral song, 1835–1849), where the reckless Lemminkainen must earn a bride from the hostess of the North by hunting monstrous game. He runs down the demon-elk until "the moose was well-imprisoned", then is sent after the "flaming horse of Hisi," a stallion breathing fire from mouth and nostrils, which he bridles under a hail of iron. But the third command is the deadly one: "When for me the swan thou killest / In the river of Tuoni" — the black death-river of the underworld. He "Braved the third test of the hero" with a single arrow, and there, hunting the swan of the dead, he is himself struck down and hewn to pieces.

Stith Thompson (1885–1976), the American folklorist whose motif-index gives this task its number, filed beast-slaying quests across Irish, Icelandic, and African tradition, and heavily through the Hercules cycle; here the Greek and Finnish witnesses carry the shape, while the others wait unread. The two diverge on one point worth sitting with: Hercules survives every beast, and Lemminkainen does not. What separates the monster-killer who comes home from the one the monster's river keeps?