Margareta Marza, a 28-year-old marketer in Stockholm, was reading a book on Thursday evening when she received my call.

Until she told me, I had no idea who she was. And she didn’t know who I was — or which number, country or time zone I was calling from. But that was the fun part.

To gin up interest in the country, a Swedish tourism agency created the Swedish Number, 46-771-793-336, a single phone line that connects international callers to randomly selected Swedish volunteers to chat about whatever is on their minds.

When I called the number and was connected to Ms. Marza, she said she had been driven to participate out of curiosity and for the chance to have pleasant, serendipitous chats.