kuchisake-onna

In Japanese mythology, the ghost of a woman who was married to a samurai. She cheated on him with another man, and when her husband found that out, he killed her by cutting a slash wound on her face that ran from her mouth to her cheek. Nowadays, she roams the streets at night with a surgeon's mask and asks random people the question "Do you think I'm pretty?". If you say no, she will mutilate you. However, if you say yes, she will reveal her full face to you. Then she will ask the same question. Again, if you say no, you will still be mutilated. If you say yes again, she will cut your face in order to make you look like her. The only known way to avoid death during a confrontation with a kuchisake-onna is by saying that she is neither pretty nor ugly or some other unexpected answer. Right after answering, throw something at her and run for your life.

The kuchisake-onna's name means "slit-mouth woman" in Japanese.