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 Post subject: Puzzle Difficulty.Posted: Thu Oct 25, 2012 3:59 am

Joined: Tue Oct 09, 2012 4:11 pm
Hi everybody I am planing to make a spreadsheet that shows puzzle difficulty.
If you would like to submit your thoughts on difficulty please post with puzzle name and your proposed difficulty (0-100 50=3x3).
Thankyou

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 4:05 am

Joined: Sun Feb 20, 2011 5:14 pm
Location: Hertfordshire, UK
I've thought on this subject many times before (I even remember a big discussion on the subject not so long ago), and always come to the same conclusion. The difficulty of a puzzle is something that is so inherantly personal to each individual that it is practically impossible to come up with any kind of useful or accurate indicator.

Things like 'time to solve' and 'minimum number of moves to solve' are indicators, but they don't really reflect a puzzles difficulty for an individual solving it.

It would be interesting to hear other peoples thoughts on the matter though.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 4:47 am

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
You can classify puzzles using number of pieces, number of faces, number of layers, number of positions, god's number and then apply them to a formula to get a difficulty rating. But you also have to factor in jumbling, super stickers, parity etc. I think that maybe you would need to take into account a dozen or so parameters to get a valid result..

And what about shape mods? A Ghost cube uses exactly the same algorithms as the donor 3x3x3 but it is much more difficult to solve.

I think that, unless you use purely subjective judgments as mentioned by Hybrid424, this may prove nearly impossible. I rate the difficulty of this task as 82

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 5:03 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
We've been down this path several times before. A 1-dimensional scalar value isn't expressive enough to capture the relative difficulties of two puzzles.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 5:06 am

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
bmenrigh wrote:
A 1-dimensional scalar value isn't expressive enough to capture the relative difficulties of two puzzles.
But the answer to life, the universe and everything (which is pretty complex) is 42

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 5:11 am

Joined: Sun Feb 20, 2011 5:14 pm
Location: Hertfordshire, UK
Gus wrote:
But the answer to life, the universe and everything (which is pretty complex) is 42

How about we all just agree now then that all puzzles have a difficulty of 42. Job done!

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Q: How many puzzles does a collector need in their collection?
A: Just one more.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 8:16 am

Joined: Sat Sep 15, 2012 7:42 am
You could do something like the Facesmash site from the movie The Social Network. In that, they created a simple website that showed pictures of two females and asked you to select which one was more attractive. If I remember correctly, it involved an ELO-type ranking. Averaged over many, many votes, they used it to create a ranking of all the females on campus. With puzzles, though, you could show two puzzles and ask users to select which is more difficult.

Might not work so well for the more rare puzzles, since fewer people have access to them.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 8:45 am

Joined: Sun Feb 20, 2011 5:14 pm
Location: Hertfordshire, UK
That's actually quite a clever idea! As a bit of fun I'd really like to see something like that, but it poses a few problems.

Setting something like that up would be a serious undertaking I'd imagine, there are a lot of puzzles out there. And as there are so many puzzles out there it's safe to say that not everyone will have solved all of them, so the odds of people randomly being asked to compare puzzles they haven't seen/tried/solved is extremely high.

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Q: How many puzzles does a collector need in their collection?
A: Just one more.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 9:58 am

Joined: Wed Jan 14, 2009 6:37 pm
Location: The Great White North
Hybrid424 wrote:
That's actually quite a clever idea! As a bit of fun I'd really like to see something like that, but it poses a few problems.

Setting something like that up would be a serious undertaking I'd imagine, there are a lot of puzzles out there. And as there are so many puzzles out there it's safe to say that not everyone will have solved all of them, so the odds of people randomly being asked to compare puzzles they haven't seen/tried/solved is extremely high.

You could just ask whether or not they have seen the puzzle before, solved it before, etc.. So you can skip over combinations involving puzzles that haven't been seen before. But yeah, you're not likely to get enough votes to rank the rarer puzzles.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 10:39 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
How does difficulty scale as the puzzle layers are scaled?

2x2x2 < 3x3x3 < 4x4x4 < (5x5x5 == 7x7x7 == 9x9x9 ...) < (6x6x6 == 8x8x8 == 10x10x10 ...)

I'd also say Megaminx < (Gigaminx == Teraminx == Petaminx ...)

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Prior to using my real name I posted under the account named bmenrigh.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 11:59 am

Joined: Wed Jan 14, 2009 6:37 pm
Location: The Great White North
bmenrigh wrote:
How does difficulty scale as the puzzle layers are scaled?

2x2x2 < 3x3x3 < 4x4x4 < (5x5x5 == 7x7x7 == 9x9x9 ...) < (6x6x6 == 8x8x8 == 10x10x10 ...)

For me, it's 2x2x2 < 3x3x3 < 4x4x4 == 5x5x5 == 6x6x6 == ...
Once you learn one non-trivial even cube (4x4x4), the rest are not much different, just more tedious. Once you learn how to solve face centers on 4x4x4, everything else is not much different (that's why 4x4x4==5x5x5).

Quote:

I'd also say Megaminx < (Gigaminx == Teraminx == Petaminx ...)

Agree here. Though I have to say that the gap between megaminx and gigaminx is much smaller than the gap between 3x3x3 and 4x4x4, because you never have to deal with parity issues.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 2:55 pm

Joined: Tue Oct 09, 2012 4:11 pm
Mabby we should go with themathkids idea.
First of all people post the names of a few common puzzles then on the 1st of November, I will take the list and pit two against each other you vote for who wins (asking and voting is repeated many times) and bam we got a result.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 3:17 pm

Joined: Mon Mar 30, 2009 5:13 pm
Its strange that people say difficulty can't be measued with just one number because it is multi-faceted, and yet we can use only one word - "difficult" - and qualify it with words like "very" and "extremely" in a linear fashion. So I don't see any reason why it can't be done...

I really like the facemash idea, though I would prefer it with girls instead of puzzles.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 3:50 pm

Joined: Wed Jan 14, 2009 6:37 pm
Location: The Great White North
Well, ELO rankings are not accurate unless enough people vote. I would think a Condorcet-type voting system might produce more meaningful results.

But anyway, that's just nitpicking. This is all for fun anyway, so here goes the list of (what I think are) common puzzles that most people here would have encountered:

- 3x3x3 (obviously)
- 2x2x2
- 4x4x4
- 5x5x5
- pyraminx
- Square One
- megaminx

Here are less-common puzzles that may be common enough to be worth voting for:
- pyramorphix
- master pyramorphinx
- tower cube (2x2x4)
- floppy cube (3x3x1)
- 2x2x3
- professor pyraminx
- gigaminx
- teraminx
- skewb (? - I don't even have one!)
- skewb ultimate
- helicopter cube
- rex cube
- 6x6x6
- 7x7x7
- face-turning octahedron
- pyraminx crystal
- master square one (forgot the official name, the one with 4 layers)

Here are some rare puzzles that probably aren't worth voting for 'cos not enough people own them (much less solved them):
- petaminx
- edge-turning dodecahedron
- vertex-turning dodecahedron
- dogic (12-color)
- ... others

Last edited by quickfur on Thu Oct 25, 2012 3:55 pm, edited 1 time in total.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 3:54 pm

Joined: Wed Jan 14, 2009 6:37 pm
Location: The Great White North
KelvinS wrote:
Its strange that people say difficulty can't be measued with just one number because it is multi-faceted, and yet we can use only one word - "difficult" - and qualify it with words like "very" and "extremely" in a linear fashion. So I don't see any reason why it can't be done...
[...]

The problem is not that you can't make a linear scale of puzzles, the problem is that everyone has their own scale, and they don't match up. Some people may rank puzzle X harder than puzzle Y, but others may rank puzzle Y harder than puzzle X. This is because the difficulty of a puzzle is mainly ranked by one's perception of various aspects of the puzzle, but everyone's perception may not be the same. Reducing everything to a single number would only work for one person (the person who made the rankings), because somebody else will find a higher-ranking puzzle easier than a lower-ranking puzzle -- because he gauges different aspects of the same puzzles differently.

But regardless, it can still be done -- for the fun of it. I wouldn't take the final rankings too seriously, though. Just because most people rank puzzle X higher than puzzle Y doesn't mean that you won't find X easier than Y.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 7:45 pm

Joined: Mon Mar 30, 2009 5:13 pm
Makes sense.

Another approach is to select a number of parameters that contribute to difficulty (no. axes, permutations, god's number, etc.), and weight them based on the average weight that people give each parameter.

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If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 10:05 pm

Joined: Wed Jan 14, 2009 6:37 pm
Location: The Great White North
KelvinS wrote:
Makes sense.

Another approach is to select a number of parameters that contribute to difficulty (no. axes, permutations, god's number, etc.), and weight them based on the average weight that people give each parameter.

Another idea is to have not a single "hardest puzzle", but award different "winning" categories, like "most number of combinations", "highest god's number", "longest algorithms needed in solution", "most different piece types", etc.. Each category would have a winner, a runner up, and a worthy mention. So not only people can see which puzzles are rated most difficult, they can also see what kind of challenges they present. I think this would be much more meaningful than a straight number. (Plus it would be more fun! I can already see petaminx winning both the "most number of pieces" and "most expensive puzzle" awards )

There can also be joke categories, like "most trivial" - award goes to the 1x1x1 cube.

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 Post subject: Re: Puzzle Difficulty.Posted: Thu Oct 25, 2012 11:53 pm

Joined: Thu Dec 15, 2011 10:04 pm
A single number, the product of the average solve time in seconds and the average number of moves in a typical solve. Call it the "challenge product", CP. For a given puzzle, the CP will be different for each solver, however I predict that for experienced solvers the values will converge. A puzzle's overall CP could be an average or geometric mean of values from experienced solvers. A puzzle's CP will fall over time until it reaches a steady state that reflects use of the most efficient solution methods.

My CP for 3x3x3 would be around 1500, but for speed solvers it could be around 200. My CP for the Teraminx would be 7.8M using an estimate of 760 moves. It should be possible to generate tables of average number of moves in a typical solve.

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