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        riddles >> easy >> ANSWERS VS. PROBLEM-SOLVING PROCESSES
        
(Message started by: william wu on Jul 27^th, 2002, 4:27pm)

Title: ANSWERS VS. PROBLEM-SOLVING PROCESSES
Post by william wu on Jul 27^th, 2002, 4:27pm

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:

http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex1a.gif http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex1b.gif http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex1c.gif
(All three are red; all ovals; all have two symbols; and all different shadings.)

http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex2a.gif http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex2b.gif http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex2c.gif
(All different colors; all different symbols; all have different numbers of symbols; and all same shading.)

and an invalid set:

http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex3a.gif http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex3b.gif http://www.ocf.berkeley.edu/~wwu/images/riddles/setgame_ex3c.gif
(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!

Title: Re: ANSWERS VS. PROBLEM-SOLVING PROCESSES
Post by oren on Aug 8^th, 2002, 4:47pm

There's a whole class (more of a seminar) here (at Berkeley) on the subject of how solve difficult problems taught by Prof. Kahan (a friggin' genius of floating point fame), Math H90. I recommend sitting in on it to anyone who wants to learn a bit about how to think.

Title: Re: ANSWERS VS. PROBLEM-SOLVING PROCESSES
Post by william wu on Aug 8^th, 2002, 4:56pm

Haha. I happen to be enrolled in that class next semester. Still debating on whether I'll have time for it though, since my other courses are pretty heavy. Maybe I'll see you in class :)

Title: Re: ANSWERS VS. PROBLEM-SOLVING PROCESSES
Post by KAuss on Nov 26^th, 2002, 12:17am

Well, since this is a sticky, dunno if it's even relavent now, but I usually think by mapping out a table of possibilities. This format usually works and for small situations usually give me a sure answer. I usually do it mentally, but when the problems goes to a hostile form into the medium sized situations then I use good ol pen n paper to do matrixes. If it gets even more extreme than that, then it's time to find a logical math equation to solve such a disaster.

Half the time is spent finding the right tools for the job, then next step is figuring out how to apply this tool to the problem...

Sometimes I think of questions while I try to find answers too, and thought this was a pretty cool ME (mech engineer) riddle, sorta like the chicken and the egg....

"Which is better? A flat head screwdriver or a phillips?"

There IS an actual answer to this believe it or not... Those mechs might know it already through experience...

Title: Re: ANSWERS VS. PROBLEM-SOLVING PROCESSES
Post by Manntis on Nov 1^st, 2005, 11:52am

the right anwer, of course, being "A Robertson"

Title: Re: ANSWERS VS. PROBLEM-SOLVING PROCESSES
Post by DewiMorgan on Jun 6^th, 2006, 9:12am

on 11/26/02 at 00:17:20, KAuss wrote:

"Which is better? A flat head screwdriver or a phillips?"

In terms of real life, [hide]it's better to have a flathead since it'll sometimes work on both. A phillps will never work on a flathead screw.[/hide]

In terms of riddles, the most satisfying answer is always the best fit, so the "driver" (answer) is always the one that matches the screw (problem). There is nothing intellectually satisfying about finding an answer that fits the preconditions of a riddle, but doesn't fit with all the facts of the riddle.

Take the (trivial) riddle:
"A large man writes three sets of letters on paper:
HCV
GBU
He scribbled out the third line. What was it?"

Now, any set of letters matches all preconditions. So "FAT" is valid, but so is "doodyhead" and "echidna". However, only "FAT" is a "good match", because it takes all things (including the order of the preceding letters, his actions and his size) into account.

This is the difference between a crosshead and a flathead screwdriver.

[Edit: fixed typo, thanks SMQ!]

Title: Re: ANSWERS VS. PROBLEM-SOLVING PROCESSES
Post by SMQ on Jun 6^th, 2006, 9:48am

Shouldn't that first line be "HCV"? ;D

--SMQ