Final answer:
Any combination of resistors can be broken down into series and parallel combinations, except for certain circuits that contain complex connections that cannot be simplified further.
Step-by-step explanation:
In general, any combination of resistors can be broken down into series and parallel combinations. However, there are certain circuits that cannot be reduced to a combination of series and parallel connections.
A circuit that cannot be broken down into series and parallel combinations is one that contains both series and parallel connections that can't be simplified further. In other words, it is a combination of resistors that doesn't follow a simple series-parallel pattern.
One example of such a circuit is a network of resistors connected in a triangular pattern, where each resistor is connected to the other two. This type of circuit cannot be reduced to series and parallel combinations.