HOW TO PROVIDE public housing without creating hellholes of crime and filth is a question that has long puzzled city officials. But now, the city's Department of Housing and Community Development appears to be finding answers. One is to disperse families in public housing throughout the city as much as possble and thereby do away with large, ugly complexes. The city already has about 500 families in publicly owned single-family homes throughout the city and plans to buy 2,000 more of these "scattered-site" units, including houses, apartments and cooperatives, during the next two years.

"Scattered-site" housing is intended to offer some alternative to the crowded, often dilapidated public housing now in the city. It is a first step by the housing department to deal with destructiveness often associated with life in public housing. The spirit of people who live in such buildings is often as much of a problem as the buildings themselves.The housing department hopes that poor people living in an economically mixed group will be more likely to care for their homes and may be inspired by example to improve their lot in life.

That idea deserves a chance. It is better than investing the housing department's current budget in the construction of more developments like those that have already failed. And the "scattered-site" housing also diffuses opposition from people who do not want to live near public housing.

In the past, public housing has ruined neighborhoods and property values with crime and garbage-filled streets.Now the housing department hopes that public housing will no longer be an isolated problem that feeds on its own problems and that it will become a healthy part of the larger community.

A second answer the housing department is offering is the eviction of tenants who are convicted of crimes committed at public housing complexes. Most often, the victims of such crimes are the building's occupants themselves. With a waiting list of about 10,000 families for public housing -- some people have waited more than five years -- the housing department can now make demands of the people who live in public housing not to prey upon others who live there is a small first step toward ending the nightmarish conditions that exist in most of the city's public housing.