Regarding difficulty for recent problems

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user202729
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Joined: Tue Dec 29, 2015 2:58 pm

Regarding difficulty for recent problems

Post by user202729 »

* While it's going to be very inaccurate for very new problems, is it possible that we can see an estimation of the difficulty of the recent problems? Waiting for 10 weeks is slow.
* Is the formula that Project Euler used to calculate the difficulty for archive problems available online?
* Otherwise, if I made a program to do that, is it okay (for the site owners/most members here) if I post it online?

Remark: the site can already calculate "unfinalized" difficulty for archive problems with less than 100 solvers, so it would not be a problem to apply it to recent problems.
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hk
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Re: Regarding difficulty for recent problems

Post by hk »

The algoritm is a linear regression on the times it took to solve the problem for the first 100 solvers, the difficulty is derived from the slope of that regression scaled to 20 steps.
Based on that information you could try to make something that reproduces the difficulty of some rather recent problems.
The reason we do not show difficulties for problems younger than 10 weeks is the possibility of irregularities for difficult problems.
Personally I think you can reasonably estimate the difficulty by looking how long it takes before the first 50 solvers are in.
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philiplu
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Location: Redmond, WA, USA

Re: Regarding difficulty for recent problems

Post by philiplu »

Also, it has been mentioned in the chat forums before that new problems are usually posted in a regular cadence of difficulty, as perceived by the development team. You'll notice on the News page on the main site that the scheduled times for new problems are usually shown in groups of 6. Those problems are, mostly, expected to be Medium/Easy/Medium/Easy/Medium/Hard. For instance, last weekend's problem, #740, was the 5th of a group of 6 and should be a medium-difficulty problem. #741, to be released this coming weekend, should be a hard problem. Looks like the News page has also been updated with the next batch of 6 problems, 742 to 747, so I'd again expect those to be M/E/M/E/M/H.

This isn't always right. Sometimes two or three problems are released together, and those are usually related and of increasing difficulty. Sometimes an extra problem is inserted, like the 1 million member commemoration (#710). And sometimes, the development team's idea of difficulty is amusingly off-base - 95% problem #589, Poohsticks, was apparently thought to be Easy or Medium :D
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user202729
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Joined: Tue Dec 29, 2015 2:58 pm

Re: Regarding difficulty for recent problems

Post by user202729 »

(it should be okay to show the difficulty for all recent problems with >=100 people solved. At the moment 8/10 of them are.)

The time to solve looks more log-linear than linear.

Some nice graphs (which can also be used to lookup/guess a problem's difficulty:

Plot of number of users / log time (seconds), colored by difficulty:

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Plot of time to 10/30/50/100 users:

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