I finally stumbled upon a formula for the Ternary Tree question. Never thought i would take three weeks! Three weeks, thinking about it several hours a day, losing sleep over it, doodling endlessly on napkins, envelopes, toilet paper, bills. Wow is all I can say.
I have mixed feelings when I hear about a student engaging this completely with a problem.
My first reaction is that I'm happy and that I empathize --- this is how I react to good problems, and I neglect my family and personal safety (wandering into traffic if I think I visualize a solution).
My second reaction is caution --- you need to balance the pleasure of finding a solution to a challenging problem on your own (there's a link on the problem-solving wiki about the connection between this experience mu-opioids), against the negative effects of being very distracted.
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I have mixed feelings when I hear about a student engaging this completely with a problem.
My first reaction is that I'm happy and that I empathize --- this is how I react to good problems, and I neglect my family and personal safety (wandering into traffic if I think I visualize a solution).
My second reaction is caution --- you need to balance the pleasure of finding a solution to a challenging problem on your own (there's a link on the problem-solving wiki about the connection between this experience mu-opioids), against the negative effects of being very distracted.
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