Implementing a Boolean function using NOR gates
When I input "evaluate (¬b&amp;&amp;¬c)||(a&amp;&amp;¬c)||(c&amp;&amp;¬d)" into WolframAlpha, it came back with the NOR minimal form:

(a↓¬b↓c)↓(¬c↓¬d)


where ¬ is logical NOT and ↓ is the NOR symbol (a.k.a. Peirce's arrow). 

However I don't know the process the program used to come up with the answer.  You might try writing out the truth table from their answer and see if that gives you any ideas.

If you're not able to use inverters, you can create those from NOR gates also.