If I'm not mistaken, this is the light switch game. Actually, it's not as complicated as it seems. It's a classic game of selection (just decide which switches are on), with one twist: the circuit load. If you understand the circuit load issue, the game isn't so bad.
Based on the opening, the circuit load is simply the number of switches that are on. This is important for the last rule. Basically, the last rule says that if the circuit load is some number X, then switch #X must be on. For example, if there are three switches on, one of those switches must be Switch 3. If four switches are on, then Switch 4 must be among them.
The other two rules are standard formal logic.
To illustrate how the circuit load applies in a question, look at question 8:
Q. 8 says that exactly two switches are on. That means (based on the last rule) one of them must be Switch 2. According to the second rule, if Switch 4 were on, then Switch 2 would have to be off. So, since Switch 2 is on, the contrapositive tells us that Switch 4 must be off... and that's your answer to the question.
Let me know you need further explanation.
- Chris