Top floor, left to right: Blacks, Grays, Blues; bottom floor, left to right: Whites, Greens, Browns.

Make a chart with two three columns and two rows, representing the two floors and the three apartments on each.

• Start by filling in the middle apartment on the top floor, where you know the Grays live.
• Now fill in all the possible places where the other families could live.
• To begin with, you know the Greens can't live on the top floor, because they'd have to live next to the Blues, which is impossible since the Grays live in the middle. But they could live in any of the bottom-floor apartments. When you've filled in all the possibilities, your chart should look like this: Top floor, left to right: Blacks, Blues or Whites; Grays; Blacks, or Blues Bottom floor, left to right: Greens, Browns, or Whites; Greens; Greens or Browns
• You can see, right away, that the Greens have to live in the middle apartment on the bottom floor, because their name is the only one in that box, so cross out "Greens" in the left and right bottom boxes on your chart.
• You don't know if the Whites live on the top or bottom floor, but you know they live to the left of the Grays, so try it out with the Whites on the top floor.
• You'll find it can't work, because if they live on the top floor on the left, the Blues must live on the top floor on the right. (You know the Blues live on the top, because they live over the Browns.) Since the Grays live in the middle, that leaves no room for the Blacks, who you know live on the top floor. So the Whites must live on the bottom floor in the left apartment. Cross out their name in the top left box on your chart.
• Start crossing out the eliminated possibilities from here on in, and you'll get the correct answer.