Project Euler: Inductive Chain Learning: Disclaimer?

[pim.mfs.0]

I started out with Project Euler in the year 2011. Under various accounts cumulatively I might have solved about 425 problems or so. I have contributed 5 problems to Project Euler (all at 5% or 10% difficulty level). As I was having an internal discussion about Project Euler Team vs Lucky Bai, the pendulum moved all over the place, but finally the pendulum has rested on the side of the Project Euler Team. At some point in the past (LilStalker) mentioned that not all Project Euler problems are meant to be solved by everybody. Statements like that go against present day democratic sensibilities. But that is the truth, the Project Euler statistics reveal that much. If you solve 108 problems you are already in the top 1%, solve 305 problems are you are already in the top 0.1%. Only 500 people have solved 477 problems or more. So, the inductive chain learning intended by the Project Euler Team may not be for everybody. But the most important thing is not solving Project Euler problems; it is discovering that so much fun is to be had by coming up with interesting things to do with mathematics and computing. Project Euler is one way to do timepass with mathematics and computing, it is not the only way or at the most appropriate difficulty level. As of today, there are only 8 solvers at Perfection. All the best to the hardcore problem solvers bent on achieving Perfection.

[hk]

Which democratic principle says that every problem should be solvable by everybody?
That is the same as saying that everybody should be able to win a beauty contest, or become a movie star, or a loving husband a surgeon an astronaut or a university professor or whatever else.

[pim.mfs.0]

The democratic principle is especially to a Dutch person is: everybody should have equal access to learning. Yes or No? Especially when the supposedly the whole point of the website is "Inductive Chain Learning"!

[hk]

What does this have to do with nationality?

[pim.mfs.0]

From what little I know of the Dutch: Dutch pride on their democracy and social system: equal access to health care and education at any level to all Dutch citizens, Yes/No?

[PierrotLeFou]

Just in case you don't know, we are in 2025.
It means that you had 14 years to solve those problems.
I registered on june 9, 2025.
I already solved 86 problems and I'm at level 3 (I don't know what it means ...)
I solved a few problems with difficulty level of 50.
I'm a retired computer programmer that learned programming at a time where algorithmic was not really teached.
I have to add that I'm totally blind.
So what is your problem?

[pim.mfs.0]

@PierrotLeFou: What I am saying is that Project Euler's setup for Inductive Chain Learning is maybe not for everybody. The example being: suppose there is a math classroom, and the teacher gives a problem to the class to solved in 'n' minutes. At the end of 'n' minutes, some students solved the problem correctly, some students got the wrong answer, and some had no clue as to how to go about solving the problem. What should the teacher do then? Should the teacher then discuss the solution to the problem to only those students who solved the problem? What about the ones who got the wrong answer, and the ones who had no clue how to go about solving the problem.

What I am saying is Project Euler is one way to build up your math and computing skills, but not the only way. Since quite a few people have put quite some effort into making Project Euler what it is, and more than a few people are more than happy the way it is, good for them. Just my 2 cents.

[hk]

Yes Project Euler is not the only way.
Project Euler never made a claim it is.
So you are fighting windmills if you think it does.
If people want to learn in another way that's fine but don't tire people at PE with your ideas.

[pim.mfs.0]

@hk: I will let you have the last word!
@pe: Thanks for kindling an enduring interest in math and computing, especially elementary number theory.

[PierrotLeFou]

@pim.mfs.0,
About your reply to my comments, unfortunately there is no teacher in the PE forum.
In fact, this forum is a kind of teacher.
You can try to find theories on the web that will help you.
Also, you can do searches such as: project euler problem xxx
There already are some solutions for many problems, or at least some guidelines to solve those problems.
I found some hints for a few problems in this way.
I noticed that, if I skipped some problems, and if I returned back to them later, I often find the solution.
Staying sticked to a problem doesn't help all the time.
And finding solutions to other problems sometimes gives ideas for previous problems.
Unlike in a classroom, you have all the time you want to try to solve problems.
We need perseverance ...

[echip]

@PierrotLeFou: What I am saying is that Project Euler's setup for Inductive Chain Learning is maybe not for everybody. The example being: suppose there is a math classroom, and the teacher gives a problem to the class to solved in 'n' minutes. At the end of 'n' minutes, some students solved the problem correctly, some students got the wrong answer, and some had no clue as to how to go about solving the problem. What should the teacher do then? Should the teacher then discuss the solution to the problem to only those students who solved the problem? What about the ones who got the wrong answer, and the ones who had no clue how to go about solving the problem.

When You say"Inductive Chain Learning is maybe not for everybody.", you forget that Project Euler problems aren't designed for everyone.

Some problems are designed for math lovers with a basic foundation, while others are more advanced and targeted at clever solvers. Some extremely difficult problems are designed for talented, genius-level solvers.

For some students who have absolutely no idea how to solve a problem, is it possible that the problems weren't designed for them? Are the problems beyond their ability? Will giving them the answers help them learn? No! Even if they could access the forums because they got the answers, I bet they wouldn't understand what those brilliant posts were about.

Giving them the answers only serves to satisfy their vanity and get their names listed in the fastest tables; it doesn't help them learn at all.

[pim.mfs.0]

@PierrotLeFou
@echip:
At some point in the past Project Euler landing page used the term "inductive chain learning" i.e. solving problems 1 through n should in theory prepare you to solve the problem (n + 1). That statement was not true then, and now, the term "inductive chain learning" does not even appear in the Project Euler About page. What appears now is: "Project Euler exists to encourage, **challenge**, and develop the skills and enjoyment of anyone with an interest in the fascinating world of mathematics." This has always been true, if you enjoy a challenge and are willing to struggle for the "A-ha" moment then yes Project Euler is definitely for you! If you are the persevering kind: good for you, all the best!

@echip:
Yes, Project Euler problems are not designed for everyone, that is the point I also finally came to terms with. In my classroom example: the teacher doesn't just give the answers, the teacher actually shows on the board to the entire classroom how to solve the problem. Now if some students cannot understand what the teacher showed on the board, then there is not much to be done, maybe they should go to an earlier class. I am not talking about someone who wants to post answers to new problems and get the on the fastest solvers board. I am talking about someone say wants to know how Problem 152 is solved even though they could not solve it themselves. I solved problems 1 through 151 with quite some internet help, but then 152 was too hard. Even after I entered the answer found elsewhere, I could not understand the forum thread, until vvenkai posted a Java solution with clear explanation. Then, I in an open-book manner reimplemented vvenkai's solution in Kotlin and was able to get the answer in under 7 seconds on a dated laptop then. Just because you cannot solve a problem on your own does not mean that when someone explains their solution, you cannot understand it. I am not talking about just getting access to answers, I am talking about someone explaining their solution in such a way that others can understand and re-implement it. Some learning does take place this way too!

[PierrotLeFou]

When I find a solution somewhere on the web, of course I try to understand it as much as possible.
But I try to convert it into another language and I often display partial results.
I do my best to find a better (meaning faster or more clear) solution.
I don't hesitate to use the BBCode in my comment at the beginning and put necessary comments in the code itself.
I usually first write my program in Python because I can put more attention to the method or algorithm instead of the syntax.
If it takes too much time to execute, I first ask to myself if my algorithm is the best or not.
If I became convinced that my algorithm is good, I convert my code in a compiled language such as C, C++ or Rust.
It happens that I use force brute to solve a problem but I'm not satisfied with the result.
I then check and try to understand the solutions of other users.
The surprizing thing (for me) is that I sometimes can solve a problem of high difficulty
(ex. solved by 3000 people) while I can't solve other problems that are supposed to be easier to solve.
We have different skills and knowledge and we don't face a problem the same way as other people do.

[pim.mfs.0]

@PierrotLeFou:
If you like Python, I believe it is one of the best languages out there to solve PE problems in. Have you ever used PyPy https://pypy.org/? With PyPy, for the most part it will be fast enough to avoid C++/Rust altogether.

[pim.mfs.0]

From the Project Euler Site:
1. However, as the problems are challenging, you may wish to view the Problems before registering.
2. The problems range in difficulty and for many the experience is inductive chain learning. That is, by solving one problem it will expose you to a new concept that may allow you to undertake a previously inaccessible problem. So determined participants will be able to slowly but surely work their way through the problems.

I would like to request the Project Euler Team to add to the above the statistic that roughly only 1 in 100 registered Project Euler users have managed to solve more than 108 problems as of October of 2025. This will set the expectations of new users that most people max out at less than 108 problems. To further manage expectations, it would be nice to add a statement to the effect - "be prepared to not be able to solve a significant fraction of the Project Euler problems".

[hacatu]

The statistics are already visible, that's why you can see them :p

I think the statement "by solving one problem it will expose you to a new concept that may allow you to undertake a previously inaccessible problem" is perfectly reasonable. Solving all the problems is probably impossible for almost everyone in the world. But on the other hand, at most of the points in the middle, where you still have hundreds of problems left, surely you can find one more that is easy enough, and then one more, and then one more.

The 1% threshhold being at 108 problems doesn't mean that 99% of people tried as hard as they could but just could not do 108 problems. Getting to 108 solves could take a reasonably talented person 100 hours or more, and there are a lot of other things people could be doing with their time. Getting to 400 solves would take a reasonably talented person thousands of hours. Solving a lot of problems takes a lot of time. If you enjoy the process, this is a good thing. On the other hand, there's nothing wrong with stopping if you don't enjoy it. The problems are aimed at people who want to spend a lot of time solving hard puzzles. The only minor complaint I really have is that VERY easy new problems are VERY rare, which is definitely discouraging for new users

[pim.mfs.0]

Solving all the problems is probably impossible for almost everyone in the world.

Would prefer if this was made a little bit more explicit in the Project Euler landing page and the about page.

But on the other hand, at most of the points in the middle, where you still have hundreds of problems left, surely you can find one more that is easy enough, and then one more, and then one more.

While this may be true, what I am getting at is: for every Project Euler registered user there exists a fraction 0.0 <= f <= 1.0, where f is the number of Project Euler problems this user can solve over a lifetime divided by the number of Project Euler problems available; this fraction has a hard upper-bound for every Project Euler registered user. For you, this fraction as of now is f(hacatu) = 698.0/962.0 = 0.725571726. Now, here comes the question: assuming Project Euler Problem Development Team does not change too much, and you don't develop math and computing super-powers, what are the odds of f(hacatu) ever reaching 0.95?

The 1% threshhold being at 108 problems doesn't mean that 99% of people tried as hard as they could but just could not do 108 problems.

Whatever maybe the reason, for over the last decade or even more - the 1% threshold has remained in the interval [101, 125]. Definitely, more people may solve the 108 or more problems, and the 1% threshold may go up slightly.

The problems are aimed at people who want to spend a lot of time solving hard puzzles.

Shouldn't this be made a little bit more explicit in the Project Euler landing page or About page.

[echip]

Solving all the problems is probably impossible for almost everyone in the world.

Would prefer if this was made a little bit more explicit in the Project Euler landing page and the about page.

It is not necessary to be made a little more explicit. Just pick a few problems and work on them, people will know that solving all the problems is probably impossible for almost everyone. (Unless he cheats)

The problems are aimed at people who want to spend a lot of time solving hard puzzles.

Shouldn't this be made a little bit more explicit in the Project Euler landing page or About page.

It is not necessary to be made a little more explicit. People will know that some questions should take a lot of time to solve after reading the problem descriptions.

I don't know what you're arguing with them about. The point you raise is completely unnecessary.

[pim.mfs.0]

Loosely speaking: a new registered user starting on a problem-solving tour through Project Euler problems is like an intellectual version of a cyclist attempting to do a Tour De France. I am not sure how many cyclists who participate in the Tour De France manage to complete the tour, but as far as a problem-solving tour through Project Euler is concerned: we can be certain that most problem-solvers will fall by the wayside at some point in time. As of October 2025 only 8 problem-solvers have achieved Perfection. We just want to let registered users who want to take a problem-solving tour through Project Euler have enough information so that their expectations are realistic.

[echip]

Loosely speaking: a new registered user starting on a problem-solving tour through Project Euler problems is like an intellectual version of a cyclist attempting to do a Tour De France. I am not sure how many cyclists who participate in the Tour De France manage to complete the tour, but as far as a problem-solving tour through Project Euler is concerned: we can be certain that most problem-solvers will fall by the wayside at some point in time. As of October 2025 only 8 problem-solvers have achieved Perfection. We just want to let registered users who want to take a problem-solving tour through Project Euler have enough information so that their expectations are realistic.

There's no need to add this nonsense information. Unless you've never participated in any problem-solving websites or programming competitions, you can't be unaware that there are always a mix of easy and difficult problems. The easy ones might be solved in a few minutes, while the difficult ones might only be solved by a handful of people. The question is, if someone doesn't even have this basic understanding and bothers ProjectEuler's administrators to add this nonsense information to the about page, then whose fault is it?