Problem:
Government of Greece wants to change the building. So they will move in building with square shape . Only demand is that every room has exactly 2 doors and doors cannot lead outside the building. Is this possible? What about a building ?
Solution
Solution:
The key idea is to color the table in two colors, like chessboard. One door connects two adjacent squares, so they have different colors. We can count the number of doors in two ways. The number of doors is twice the number of white squares and it is also twice the number of black squares. This is, of course, impossible, because we have one more black square on the table. So, if is odd, we cannot achieve that every room has two doors.
For table this is possible, and one of many solutions is presented on the picture below.
Figure 14
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