Question 179
Suppose there are 3 islands each for 3 different colors, red, blue and yellow. Try to build several bridges so as to satisfy the following conditions:
* For any pair of islands, they are either connected by a bridge or not connected by any bridge, and every bridge connects two distinct islands.
* For any pair of islands of a same color, there is no bridge connecting the pair, and furthermore, there is no island which is connected to both of the islands in the pair by bridges.
How many ways of building bridges to satisfy these conditions? Building no bridges will be counted as one possibility.
* For any pair of islands, they are either connected by a bridge or not connected by any bridge, and every bridge connects two distinct islands.
* For any pair of islands of a same color, there is no bridge connecting the pair, and furthermore, there is no island which is connected to both of the islands in the pair by bridges.
How many ways of building bridges to satisfy these conditions? Building no bridges will be counted as one possibility.