The House Where She Lives

           It was at a cocktail party in New York that I met Stephanie. We exchanged our phone numbers and decided to meet each other soon.

          When she rang up and invited me to her house this is how she gave me the number of her house.

I live in a long street. Numbered on the side of my house are the house one, two, and three and so on. All the numbers on one side of my house add up to exactly the same as all the numbers on the other side of my house. I know there are more than fifty houses on that side of the street, but not so many as five hundred 

          Can you find Stephanie’s house number?

Answer:   The numbers of the houses on each side will add up alike if the number of the house be 1 and there are on other houses, and if the number be 6 with 8 houses in all, if 35 with 49 houses, if 204 with 288 houses, if 1189 with 1681 houses and so on. But we know that there are more than 50 and less than 500 houses, and so we are limited to a single case.

                The number of the house must be 204.