Genevieve Piturro is engaged in a special pajama game for needy children.

It involves arithmetic and sociology.

Here’s a question from the game: If 500 children’s institutions around the country have signed up to receive pajamas from Ms. Piturro’s nonprofit organization, Pajama Program Incorporated, and there are 35,000 pairs to give away each year, how many does each institution receive?

Seventy?

Wrong.

That’s because different institutions – orphanages, hospitals, and childcare centers – have different populations.

Consider this as well: If Mr. and Mrs. Smith, a poor couple, write to Ms. Piturro asking for pajamas for their four children, should the Yonkers-born entrepreneur oblige?

Of course, you may say.

Wrong.

That’s because the demand for pajamas is so heavy that Ms. Piturro can fulfill requests only from institutions.

“It breaks my heart that for so many underprivileged children, nighttime often means a hard end to an equally hard day – many go to bed wearing their street clothes, or wearing nothing at all,” Ms. Piturro said. “At any given time, there are more than 5,000 children’s institutions on my waiting list.”

A predicate of her pajama “game,” of course, is that there will always be a waiting list. In Westchester, for example, more than 30,000 children – ranging from infants to 17-year-olds – are said to be living below the poverty level. The Coalition for the Homeless says the number of children in New York City shelters is nearly 13,000 and growing.

Such depressing statistics flow from a skewed economic system that many scholars argue has become too complicated for quick fixes. Ms. Piturro says she isn’t pursuing solutions to the big problem of societal inequities as much as focusing on the specific needs of poor children.

Ms. Piturro is no podium-thumping crusader. Her emphasis is on coming up with solutions, something she learned during her long years in the communications business.

It was during those years that Ms. Piturro became engaged with charitable work at hospitals and orphanages.

“The turning point came right after September 11, when, on the spur of the moment, I decided to buy a dozen pairs of pajamas, instead of toys, to give to some children,” Ms. Piturro said.

She took those pajamas to an afterschool program for abused children in Spanish Harlem.

One little girl, delighted at the gift, asked Ms. Piturro: “What are these?”

In that instant she said she realized how many poor children had never had pajamas.

“I realized how important it was to create a warm and nurturing environment for children, the kind of environment my parents gave me when I was growing up,” she said. “By giving pajamas, and also books, I hoped that I was conveying to the children that somebody out there cares.”

The idea of offering such caring was central to the organization that Ms. Piturro started in late 2001, the Pajama Program.

“I found myself carrying 10 or 15 bags of pajamas to distribute to children each week, so I said to myself, ‘Why not create a mechanism for this?'” Ms. Piturro said.

That “mechanism” was initially housed in her Riverdale living room, where Ms. Piturro and her husband, the actor Demo DiMartile, would sort out pajamas that they bought and package them.

“I always thought that children appreciate new things, so I decided from the start that I would distribute new pajamas rather than used clothes,” Ms. Piturro said. “I started modestly, but soon found out that there was a huge demand.”

Since that start five years ago, Ms. Piturro has distributed more than 60,000 pairs of pajamas, and nearly 70,000 books. She has established chapters in 13 states, although the pajamas are sent all across America. Pajamas and books also go to 15 countries, including Armenia, Brazil, China, Iraq, South Africa, and Ukraine. Those pajamas and books are frequently donated by schools, mothers’ clubs, women’s groups, book clubs, churches, libraries, businesses, and scout troops.

Ms. Piturro also obtains donations from pajama manufacturers such as Lands’ End; Richard Leeds Interna tional; SkivvyDoodles/My Boy Sam; St. Eve; Waterbury Garments, and Greggy Girl. And donations regularly come in from many publishers, including Scholastic; St. Martin’s Press; Lee & Low, and Workman Publishing.

Contributions have been coming from even the corporate world. Pfizer, JPMorgan Chase, and Verizon, for example, have year-round drives to collect pajamas, which are then delivered in special boxes to Ms. Piturro.

“The fact that big companies are engaged in helping children secure such elementary comfort tells me how bighearted America’s corporate world is,” Ms. Piturro said.

She pointed to assistance from RD Weis Companies in Port Chester when Hurricane Katrina struck last year. The flooring manufacturer donated a van to Pajama Program, and also sponsored two trips to the affected region. Ms. Piturro helped distribute more than 11,000 pairs of pajamas, and thousands of books.

In advancing her work, she reaches out to celebrities such as Patti Labelle, who last Friday was named “Mother of the Year” at a luncheon fund-raising event at the Pierre.

Ms. Piturro even got Microsoft to chip in.

“They donated $69,000 worth of software,” Ms. Piturro said. “Now we need to raise enough money to acquire computers, so that we could create a network for all our national chapters. My pajama game never ends because the needs are always continuous.”