What is the diligent search for an answer or a solution to a problem called?

is a diligent search for an answer or a solution to a problem.

Research

Explanation:

Research is a deliberate attempt to find answer or solution to a problem along with help of observation, study, survey, comparison, literature review and experimentation.  

It is in other way a search for knowledge through systematic way of finding solutions to a problem.  

The research methodology comprises of following stages –  

Stage  I – Observing a problem

Stage II – Formulating a hypothesis

Stage III – Collecting the data

Stage IV – Analysis of facts and data

Stage V – Finding a solution or reaching a conclusion

i believe it is "they are not used up by reactions" as the answer to your question, text me back if this is correct because i just learned this.