Ride South to Purgatory by Work, James C.

When Pasque Pendragon comes to live at his uncle's ranch in the Wyoming Territory, his mission is to track down the killers of his brothers. But everything changes with the arrival of a stranger at the ranch Christmas party. This giant of a man issues a bizarre challenge: He will fight a duel in which any man may fire three shots at him point-blank. But if the three miss, he may be able to do the same to him in a year's time. Pasque accepts. To his horror, he misses and the stranger rides off into the night. Thus begins the consuming passion of Pasque's life and his journey to find the ominous giant.