Suppose a system of two particles, represented by circles, have the possibility of occupying energy states with 0, 10, or 20 J. Collectively, the particles must have 20 J of total energy. Are there any other energetically equivalent configurations?

Explanation:

The possible energy states for the particles are 0, 10 and 20 J.  

The constraint in the system is that the total energy of the particles must be 20 J.

One given configuration where the total energy is 20 J is if both the particles occupy the 10 J state.

Hence, (10;10) is the given configuration.

Another possibility is if one of the particle is in 0 J state and another is in 20 J state. Hence, the system has a total energy of 0+20 = 20 J.

Hence, the possible configuration can be written as (0;20) or (20;0) which are energetically equivalent to the given configuration. Note that if the circles are indistinguishable, then the configuration (0,20) and (20,0) is the same thing.