However, using a solution after you have genuinely attempted the problem for 45 minutes is . You check the solution, find where your logic broke, and then re-attempt a similar problem from scratch. The Best "Solution" Is Persistence I have watched dozens of students hate thermal physics in September only to fall in love with it by December. The turning point is always the same: the moment they stop searching for answers and start constructing their own.
If you are an undergraduate physics student, you have likely encountered the holy grail of thermodynamics and statistical mechanics textbooks: Concepts in Thermal Physics by Stephen J. Blundell and Katherine M. Blundell. Blundell And Blundell Concepts In Thermal Physics Solutions
So, treat the Blundell problem set like a gym session. The "pain" of the derivative is the "gain" of the intuition. When you finally derive the Planck distribution from first principles, the feeling is electric. However, using a solution after you have genuinely
Read the problem and write down physically what is happening. Is this an isolated system (microcanonical ensemble)? A system in contact with a heat bath (canonical)? Are particles distinguishable? The turning point is always the same: the