(a little philosophizing...)

After Federico Kereki's puzzle Get one half by squaring was posted and solved, I sat back and wondered to myself, "Why did I feel this puzzle was so great?" So here are my thoughts on the question, "What makes a great puzzle?":

1. The problem statement must be understandable, well-defined, and accessible to the average person. (e.g., no problem that requires advanced mathematics to state)

2. The solution must be easily verifiable by the average person. (e.g., ruling out most solutions that depend on advanced mathematical proofs)

3. An intelligent person should be able to spend hours on the puzzle, feel that he/she has made progress, even without having solved the puzzle. This progress can be of the form of narrowing the search space (i.e., eliminating possibilities in chess puzzles). This rules out "hit-or-miss" puzzles, where no real work (either leading to the solution or not) can be done in the set (search space)-(solution set).

4. The problem should thwart "brute-force" techniques (esp. computer programs), either via a large (possibly infinite) search space or via the requirement of exceptional creativity (within the bounds of the well-defined-ness of the problem statement) that a "brute" would miss (smile).

5. Even knowing the solution, one should not be able to justify why the approach taken would necessarily lead to the solution. In other words, I can say, "I solved this by trying XYZ...", but I should not be able to say, "This method was bound to work because ABC..." This shroud of mystery I believe is necessary to distinguish puzzles from math problems, though there is a large overlap between the two.

Any thoughts? Agreements, counter-examples, other criteria?

I think a good puzzle is one that captivates your interest immediately but takes a while to figure out. I can't be too hard so that you give up in frustration but it needs to be somewhat elusive to give it appeal

i like puzzles that are interesting that can keep me busy for awhile withought frusterating me.

I am a programmer and I agree with you, Bruce.

Interesting...I am a pretty serious programmer myself, and I usually consider puzzles with an easily programmable solution an "inferior" brand...I liken it to presenting a word puzzle to an audience that includes non-native English speakers. I suppose if the puzzle is written with the intent of being solved by computer (Conversing Club 3, I assume), then that makes it different. But IF a puzzle is intended to be solved without computer, the existence of an easier computer solution is, in my mind, always an undesirable trait.

As far as "12 dots (and more)", Bruce, I simply drew some dots on the page and got lucky, I suppose. I just knew how to think outside the box from having seen the more famous 3x3 puzzle with 4 lines (not ending where you started, though).

I don't know that this is the right place to discuss such a question.
Rather than give the solution I will give a pointer.

Try finding the solution for the first few whole numbers. Then either look for a pattern or check the OEIS

http://www.research.att.com/~njas/sequences/Seis.html


-Jer

Lately I have been working on a slightly different philosophical problem; how does one create inviting scenerios that are particularly ripe/suggestive for posing problems? Great puzzles stimulate those who have an interest in such, but oft times the key to developing budding reasoning skills is to encourage one to ask their own puzzlers. It is amazing how this can broaden a person's range of what they consider "interesting". But I know the intent here was not an education discussion :-)

Anyway, as far as interesting puzzles, I look back on my last several personal perplexus tangents, and they are all instigated by problems posed by Shin. I guess that philosophizing is working :-)