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Topic: ANSWERS VS. PROBLEM-SOLVING PROCESSES (Read 4638 times) |
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william wu
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ANSWERS VS. PROBLEM-SOLVING PROCESSES
« on: Jul 27th, 2002, 4:28pm » |
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First of all, thanks to everyone for visiting! I'm truly thrilled by the activity of this bulletin board, and there are some very interesting discussions.
Now, there have been a few threads recently that are just lists of answers. This doesn't bother me terribly -- actually, I appreciate it to some extent since it lowers the in-flux of e-mail I get from tortured minds. However, I'm not sure how useful it is to tell someone only an answer.
As an analogy, this summer my friend Hansen introduced me to an extremely cool card game called Set (www.setgame.com). There's a deck of 81 cards, each card varying across four variables: color, symbol, shading, and number. Given 12 cards, you want to find 3 that share the same patterns. (Kind of like the pattern matching problems on some IQ tests.) Specifically, you want to find a 'Set', which is a group of 3 cards in which each variable is EITHER the same on each card, OR is different on each card. That is to say, any variable in the 'Set' is either common to all three, or is different on each card.
Examples of valid sets:
  
(All three are red; all ovals; all have two symbols; and all different shadings.)
  
(All different colors; all different symbols; all have different numbers of symbols; and all same shading.)
and an invalid set:
  
(All different colors; all diamonds; all have one symbol; however, two are open and one is not.)
When you play Set with others, you're just trying to find sets faster than everyone else. During my first few games, I remember feeling astounded by my friend's thinking speed. Hansen had written a C++ program that runs the game, and we were staring at the monitor, our hands poised to pounce on the mouse between us.
He'd point to three cards. "See, this is a set." I'd look at them, notice the pattern, and then say "Ah, yes, I see." He'd click the cards, and 3 new ones replaced them.
A few seconds pass. "Now this is a set." Click, click, click, refill. "I see."
"This is a set." Click, click, click, refill.
"Set." Click, click, click, refill.
"Set." Click, click, click ...
I'm sitting there with glazed eyes, nodding my head, just verifying that his answers are correct, rarely having ample time to find my own sets before the electric cards refresh.
Afterwards, I asked Hansen how he thinks about the game. Do you try to match cards in a certain order -- for instance, first by number, then color, then shape and then shading? Is it just a really fast depth-first search? Or do you run it all in parallel? I had realized it was both trivial and useless to verify the correctness of his sets. What I wanted to know was how he finds sets so quickly in the first place!
Hansen said he would explain his thought processes at the end of summer. In the meantime, the game would be more educational if I developed my own approaches and shortcuts. He gave me some pointers to get started. Now that summer is drawing to a close, I feel comfortable with my playing ability, and it's not very important whether or not he explains his methods, because I have my own.
Conclusively, it's far more meaningful to generate an answer than it is to verify it. That's the difference between checking a set and finding it, between telling a joke and laughing at it, between eating a fish and learning to fish, between checking an NP problem and actually solving it. There will always be new puzzles and problems, and definitely not just during Microsoft interviews. So when I surrender to a riddle and ask for help -- and this does happen often -- I don't just want an answer. I'd like a problem-solving thought process. I want to know how a person goes about generating such an answer. What branches of thought were explored to get there. What initial observations and "hooks" did you start with? Did you think about the problem this way? Were you inspired by something peculiar? Maybe you were peeling an orange and realized that you can travel west to get east? You were drinking a glass of water and tilting it toward your mouth? You were traveling in a plane and noticed you had to set your watch backwards? We talk to ourselves when we attack these problems. What was your dialogue like? I don't just want to know your answer. I want to be cunning. I want you to teach me how to think. Because that will get me far more mileage than a hashtable of specific puzzles and their solutions.
These are my opinions about the nature of discussion that I would like to see. Sorry if I was too pedantic. Enjoy the site!
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Riddle_Pirate
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Re: ANSWERS VS. PROBLEM-SOLVING PROCESSES
« Reply #1 on: Jun 18th, 2005, 11:22pm » |
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Thanks for the new game! This should improve my already stunning pente powers. 
C++ version you say? Would you be planning to release your version anytime soon?
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pcbouhid
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Re: ANSWERS VS. PROBLEM-SOLVING PROCESSES
« Reply #2 on: Nov 20th, 2005, 6:54am » |
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William,
You wrote exactily what I think. Whenever I submit a problem in one site in England (where I´m a regular contributor), I always add a note: "Show me your reasoning". I ignore the postings that only gives the answer, and from now on my note will be: "I don't just want to know your answer. I want you to teach me how to think." Perfect!!!!
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Don´t follow me, I´m lost too.
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