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
- 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
- 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
- Start crossing out the eliminated possibilities
from here on in, and you'll get the correct