Some problems are more moves.
Some problems are uncommon patterns.
Some problems require long calculation to verify.
Some problems have common patterns that are not solutions, which distract the solver from finding the real solution.
Why are some problems harder than other problems?
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Dec 24, 2014
0
#3
I'm definitely not laughing: this is an extremely insightful question, and it is the exactly the same question I asked myself when working on tactics, which led to my idea of a certain type of computer-based tactical practice that I hope to code someday, maybe next year. leiph15's assertions are all correct, but I claim there is still much more to this problem than he mentions.
Some problems are more moves: What about puzzles of the same move length? Some are harder still.
Some problems are uncommon patterns: Why are some patterns harder than others?
Some problems require long calculation to verify: Give me an example.
Some problems have common patterns that are not solutions, which distract the solver from finding the real solution: That doesn't mean its harder. It just means the solver wasn't smart enough to see that the pattern wasn't correct.
chessmicky wrote:
Because some problems are harder than other problems. Doesn't your question answer itself?
Don't talk nonsense.
megadroid wrote:
Some problems are more moves: What about puzzles of the same move length? Some are harder still.
Some problems are uncommon patterns: Why are some patterns harder than others?
Some problems require long calculation to verify: Give me an example.
Some problems have common patterns that are not solutions, which distract the solver from finding the real solution: That doesn't mean its harder. It just means the solver wasn't smart enough to see that the pattern wasn't correct.
Any study is a good example.
Here's one I was happy to have found the solution only looking at the diagram. First I'll show the main difficulty white has. (And if the knight moves, then Kg7 and the pawn is lost eventually).
The solution I'll give in white text below. The first move only makes sense if you've seen all the way to the 6th move. The 6th move only makes sense if you've seen to the 8th.
1.Nf4 gxf4 2.h8=Q Bg6+ 3.Ka1 Be7 4.Nf3 Bf6+ 5.Ne5+ Ke7 6.Qh4 Bxh4 7.Nxg6+ Kf6 8.Nxh4
move 6: now we see the reason for the first move. This was not possible with a pawn on g5.
move 8: After the fork white is a piece up!
White text here ^
Sqod wrote:
I'm definitely not laughing: this is an extremely insightful question, and it is the exactly the same question I asked myself when working on tactics, which led to my idea of a certain type of computer-based tactical practice that I hope to code someday, maybe next year. leiph15's assertions are all correct, but I claim there is still much more to this problem than he mentions.
Like what?
I don't think my answer is perfect, I want to know others thoughts about it.
megadroid wrote:
Some problems are more moves: What about puzzles of the same move length? Some are harder still.
Some problems are uncommon patterns: Why are some patterns harder than others?
Some problems require long calculation to verify: Give me an example.
Some problems have common patterns that are not solutions, which distract the solver from finding the real solution: That doesn't mean its harder. It just means the solver wasn't smart enough to see that the pattern wasn't correct.
Isn't it harder to solve if you have to be smarter to solve it? 
But that wasn't was I meant anyway. Good players will see it's not correct, but it takes more work, because almost certainly they'll have to first calculate why these red herrings don't work before they can start verifying the winning move.
Oh yeah, that's another good one. Some have many different defenses and you have to see why each of them doesn't work.
And what I mean by making a distinction between having more moves and needing more calculation to verify is that some you solve without having to calculate all of it. You simply have to realize e.g. an attack is overwhelming. Maybe you only need to find 2 or 3 moves, and you're done (even though the resulting attack may have dozens of variations before mate).
Others (as posted above) you absolutely must see to the end to know that it will work.
Most attacks are a mix of both, but that's my reasoning in making them two separate items.
Dec 26, 2014
0
#12
leiph15 wrote:
but I claim there is still much more to this problem than he mentions.
Like what?
Just a few more things that change the degree of complexity of a problem:
1. average amount of fanout per move node (number of responses)
2. presence of captures
3. presence of promotions, including unusual underpromotions
4. newly opened lines of attack
5. reliance on rare tactical motifs (such as a newly created pin)
6. importance of lines of protection
7. preliminary analysis of the situation
8. possibility of castling
9. Zwischenzugs
You first have to define what you mean by "harder". One simple definition of harder would be, take a simple random sample of chess players and present them each with two problems in random order. Give them the same amount of time to discover the optimal move for each of the problems. If, on average, one of the problems is solved less often than the other (or in more time in the case where both problems are solved by the same number of participants), then we can say that problem is harder. Given this definition, one obvious reason why one problem might be harder than another would be that it has more legal moves to consider. Another common reason for a puzzle to be harder would be that it exploits preconceptions or processes employed by chess players which are, in most cases efficient and effective. If it's a computer solving the problem though, it will likely come down to the number of legal moves available in the initial and subsequent positions, as well as the presence of forcing sequences. Although computers employ heuristics when evaluating moves, the principal advantage computers hold over humans is they are fast, accurate and relatively indiscriminate when it comes to choosing candidate moves. I notice that nobody mentioned the rectilinear distance from the center of action (often the opponent's king) to a piece essential to the solution of the puzzle. This has no effect on a computer, of course, but has a surprising effect on humans for whom "tunnel vision" is a common malady.
Dec 26, 2014
0
#14
megadroid wrote:
1 Some problems are more moves: What about puzzles of the same move length? Some are harder still.
2 Some problems are uncommon patterns: Why are some patterns harder than others?
3 Some problems require long calculation to verify: Give me an example.
4 Some problems have common patterns that are not solutions, which distract the solver from finding the real solution: That doesn't mean its harder. It just means the solver wasn't smart enough to see that the pattern wasn't correct.
(Numbered for reference)
1) Yes, but they have one of the other elements of a hard problem. That's why this wasn't the only item on the list.
2) He just told you: Because they are uncommon. You recognize patterns more if you see them more.
3) http://www.chess.com/forum/view/general/the-problem-computers-cant-solve I think this takes quite a bit of calculation. But, it's also a long problem. Here's one that might take a small while even though it's only mate in 1, because you have so many potential moves to choose from: http://www.chess.com/forum/view/more-puzzles/mate-in-one-move2
4) Now you're just trolling. "It wasn't hard, you're just stupid for not seeing it, even though everyone else had the same problem"?
Jan 6, 2015
0
#15
The following puzzle is a good example of what I meant by "high average fanout" in the move tree. The winning line is only 3 moves deep (no mate yet, though) but I count about seven good candidate moves (Nxh6+, Nf6+, Bxg7, Bb4, Rxg6, hxg6, Rxf8+) even for White's first move of the combination, and each of those has to consider several responses by Black. I finally gave up on the puzzle due to lack of time. I knew I could solve it, but I just didn't have the time to explore every branch stemming from each of those several candidate moves. High average fanout is one of the main things that makes a chess problem harder than usual.
Source:
Page 87 of: Wilson, Fred, and Bruce Alberston. 2004. 303 Perplexing Chess Puzzles. New York: Sterling Publishing Co., Inc.
(Please allow 15 minutes for me to correct inevitable errors in this post.)
Why are some problems harder to solve then other problems? Please don't laugh at this question.