During the late Warring States period, the weak Yan state was often bullied by the powerful Zhao state. To counter Zhao, the King of Yan sent Crown Prince Dan to Qin as a hostage, hoping to form an alliance. But Qin proved untrustworthy, joining forces with Zhao instead. Zhao seized many Yan cities, even gifting some to Qin. Hearing this in Qin, Crown Prince Dan was stricken with anguish, as if pierced by a knife. King Ying Zheng of Qin, favoring Zhao, treated Dan with cold arrogance, making his days even more unbearable.
The crown prince of Yan, unwilling to remain a hostage in the state of Qin, sought an audience with the King of Qin and requested permission to return to his homeland.
The King of Qin heard this and said coldly, "When the crow's head turns white and the horse grows horns, then you may return to your country." Crown Prince Dan of Yan said indignantly, "Isn't this deliberately making things difficult?"
The King of Qin, without a word, waved his hand and dismissed Crown Prince Dan of Yan.
Prince Dan of Yan returned to his quarters, glanced at the crows in the courtyard trees and the horses in the stable, then looked up to the sky and sighed deeply, "Heaven, let me return to the state of Yan!"
Strangely enough, at that very moment, the crows in the trees turned white, and the horses in the stables grew horns.
Prince Dan, overjoyed, rushed to report this to the King of Qin. The king, skeptical, sent someone to Prince Dan's residence to verify, and indeed it was true. Left with no choice, the king reluctantly agreed to let Prince Dan return to his home state.
Though the King of Qin had agreed to let Crown Prince Dan of Yan leave, he was still reluctant to let him go. So, he rigged a trap beside the bridge the prince would cross—a mechanism designed to collapse the bridge when horses and men passed over. But when Crown Prince Dan crossed, the mechanism failed, and the bridge did not fall.
The King of Qin ordered border guards to prevent Crown Prince Dan of Yan from crossing. Arriving at the pass at night, Dan found the gates still shut, so he imitated a rooster's crow. Nearby roosters heard and joined in, fooling the guards into opening the gates, thinking dawn had come. Disguised in tattered clothes, Crown Prince Dan slipped through under cover of darkness.
And so, Crown Prince Dan of Yan finally managed to escape back to the state of Yan.
Later, the idiom "A Crow Turns White, a Horse Grows Horns" came to refer to something impossible or a wish that can never come true.
Source: *Yan Danzi*
Meaning of the Idiom: Later, the Chinese idiom "乌白马角" came to describe how something impossible or a wish that can never come true.