COPENHAGEN — In Greenland, a quarter of all police reports of child sexual abuse come from the remote district of Tasiilaq, a tiny community of 2,800 on the country’s east coast, according to the police.

Pay days are the worst time for the children of Tasiilaq, officials say. With their salaries or social benefits in hand, many adults tend to drink and parents become too inebriated to look after their children, officials say. That’s when an already high rate of sexual abuse rises, according to a police study published last week.

So on the last Friday of every month, officials open a sports hall in the district as a shelter to keep children away from sexual abuse.

“Children were abused by their stepfathers, cousins and by the neighbor looking after them as the parents were on a bender,” Naasunnguaq Ignatiussen Streymoy, the mother of a sexual abuse victim and an anti-abuse activist, told Weekendavisen, a newsweekly, in an article published on Friday about the crisis.