Of course my brain gets tired when I'm faced with chess problems like my body gets tired when I shift 15 tons of coal. I've learned from experience what to do when I feel tired. I can either push on if I'm interested enough and feel close to a solution, or I can set the problem aside and either return to it later or let it gather dust. Surprise, surprise, some problems have no solutions
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Suppose you are studying a chess book, and you are a bit stressed because you know you should be doing something else. You are focusing very hard on a puzzle whose solution is eluding you. It is 5 hours before your normal bed time. In this situation, would your brain ever suddenly feel tired or sore or just need a break? Or would you just be more likely to get bored or annoid or want to see the answer?
My other question, if it does suddenly feel tired, is what is the best way to make it stronger? Take a break and try again? Keep going? Is it like a regular muscle in that it can be overworked? Or is the most you risk that you won't get as much work done without breaks?