Easiest or most popular?

[albert]

Sometimes I get the impression that a particular problem gets a lot of solutions because it is an attractive problem, not because it is easy. That is my impression for e.g. the flea circus 217, that is probably far more difficult than 240 next to it.

Then of course newer problems look more difficult, because there has been less time
to solve them.

So in order to determine the difficulty of a problem, the number of submitted wrong
answers could be taken into account. A submitted wrong answer with no following correct answers is indication of given up, a strong indication of a hard problem.
100 good answers, 10,000 wrong answers 500 given up or working on it: hard problem
100 good answers, 10 wrong answers, 0 given up : unattractive problem

At least this statistics could provide some feedback for the inventors of problems.
I personally would love to know the total number of answers submitted besides the number of succesful answers, like in 83/170 or 83/23%

OTOH the percentage of people that bothers to do a write up is an indication of the
attractiveness of a problem.

Groetjes Albert

[TripleM]

I think you have things backwards a little bit. If a problem has lots of wrong submitted answers, that doesn't mean it is hard - in fact, a problem with 10000 wrong answers probably means the problem is *easy*.

Nobody submits a solution to a problem unless they have believed that they have solved it; submitting a wrong answer means one of three things:

a) You have misinterpreted the problem
b) You have solved the problem but there is a bug in your code
c) You believe you have solved the problem, but your algorithm is plain wrong and the true problem is a lot harder.

Only c) is related to the difficulty of the problem, and to be honest I don't think it would occur much. The 'small' input provided in problems nearly always guarantees you are working on the right algorithm. That only really leaves b) as a reason for incorrect submissions, so the number of wrong submissions is basically a measure of how good a particular person is at debugging their code. Since so many people have gotten that far, it means the problem must be pretty easy, but with some possible special cases that haven't been picked up.

So, while it would be interesting to see the number of wrong submissions, it should certainly not be taken as a measure of the difficulty of a problem. At least, that's my opinion.

[albert]

Suppose you have two problems with 100 correct solutions:
the first one everybody has correct at the second attempt, but mostly at the first attempt
the second one requires on average 5 attempts.

I find it hard to not interpret that the second problem is harder.

I feel even stronger about those who give up, i.e. don't succeed give
the correct answer within two months of their first answer.

Groetjes Albert

[hk]

Suppose one of the two problems is 9 months old and the other 2 weeks. Both have 100 solvers.
Does your reasoning still hold?

[albert]

Suppose one of the two problems is 9 months old and the other 2 weeks. Both have 100 solvers.
Does your reasoning still hold?

Yes.