Project Euler Forum

I just looked at Problem 820 of Project Euler. This problem is a very reasonable extension of Problem 26. That is when I stumbled upon the idea: I would like there to be more problems like Problem 820 (not necessarily subject-wise, but difficulty-wise.). So, would it be possible for the Project Euler problem team to take requests/votes about the kind of problems the users/solvers at the Project Euler Website want? My take is that there are already enough difficult problems on Project Euler, so why try to come up with more hard problems like Problem 585? Let's solve more problems like problem 820. If it were up to me all future problems would be at difficulty 30% or less. This is my personal opinion; others may voice their opinions.

Also, for problem 820, could it not have been split into Problem 820A and Problem 820B. Problem 820A is just Problem 820 with N = 100000, this can be solved with some extension to the method used to solve Problem 26. Then, problem 820B comes with a hint saying, the method that works for Problem 820A will not work for Problem 820B (something clever is needed (like Problems 18/67)). This gives a gradual approach to solving/enjoying problem 820.

What is the solution to Problem 585, but a whole bag of tricks which only about 215 people have been able to put together in around 10 years. What inductive learning is to be had by someone who can or cannot assemble the bag of tricks needed to solve Problem 585? Can Project Euler problem development team take a more graduated approach to the bag of tricks needed to solve a problem?

Just to state the obvious, PE is a benign dictatorship, not a meritocracy or a democracy. (Not that I'm saying that the benign dictator doesn't deserve it: rather that there's no ability test which gives the right to supplant him).

Also, democracy doesn't necessarily mean that everyone's vote is equal. If the question is about the type of new problems made available, there's a utilitarian argument that people who have fewer unsolved problems, and thus more need of new ones, should have greater weight given to their vote. I think you can see where that ends up...

Well, the title of the thread was just to grab attention. Let's see, people who solved about 125 problems or more are in the top 1% of solvers. So, I would say why care about the top 1% of solvers, lets care more about the lower 99% of the solvers. It is time to "Occupy Project Euler", the lower 99% needs to be heard by the "benign dictatorship".

It would be nice for more problems that are on the easy side to be published. The problem is that, for that to happen, those problems need to be written. As someone who has written a handful of the problems myself, I think that it's just much more difficult to come up with interesting problems which are also easy to solve. If a problem is really interesting then a lot of the time it just ends up being pretty tricky. This isn't to say that there aren't easy problems which are also really good and interesting, just that they seem to be less common, and require very thoughtful design.

Maybe you could be the change you want to see in the Project Euler problem set? Try writing some easy problems yourself and submitting them. I know they're more in need of those compared to the harder problems, which have an enormous queue for publishing.

(Also, the idea of only publishing easy problems from this point on seems a bit silly to me... people really like solving the difficult problems, and the site would probably lose a lot of its most dedicated userbase.)

I have submitted 5 problems to Project Euler all of them less than 20% difficulty. Yes, easy problems need to be written, you are correct. What I was thinking was (I peeked at the solution to problem 585), instead of publishing Problem 585 as is, could it not have been broken up into three or four problems each illustrating a method/algorithm that when put together solve problem 585. We can take hard problems and break them down into simpler problems. I am not a believer in Intelligent Design or Irreducible Complexity . Actually, I take it back, there are some methods/algorithms needed to solve Project Euler problems which would be very hard, if not impossible for an average-or-even-above-average Project Euler problem-solver to come up with. For example, we need to count some tuples with a certain GCD property for Problem 585. How did the Project Euler problem development team think that an average-joe Project Euler solver is ever going to come up with that method/algorithm unless they have seen it before or read about it in a book or webpage or YouTube video?

Are you sure people like solving difficult problems? I for sure don't. While tongue-in-cheek, 99% of Project Euler members/users/solvers have solved less than 125 problems. Are you sure they all appreciate something as hard as Problem 585? I am talking about problems that have been out there for about ten years or so and have less than 256 solvers (i.e. the number of solvers fits in an unsigned byte). I am not saying hard problems should not be published, if you have the chops to be one of the 215 who can put together the methods/algorithms to solve problem 585, good for you! The term hitting-a-wall-on-Project-Euler is there for a reason. I believe moderate difficulty problems keep a much larger userbase of Project Euler interested and active. Also, the single player game experience mentioned by euler is probably not a good idea. (Hopefully) Soon enough generative AI is going to catch up to Project Euler problems. I believe collaborative problem-solving (especially if you have a good group of people to work with) leads to more learning than a lone ranger approach.

This is besides your point, but while problem 585 is a hard problem, its difficulty is certainly not unreasonable when compared to other problems on this site. Solving problem 585 doesn't require obscure or esoteric knowledge. All the techniques needed to come up with a fast enough algorithm are explored in other easier problems. If someone has solved many other problems on the site, then 585 should be hard but very doable.

I agree with you that I hope they keep publishing easy problems. However, the demand for hard problems is there too.

Agreed that Problem 585 is solvable by methods that are not obscure or esoteric, and some of those methods, if not all of them are explored in other Project Euler problems. Still, after about ten years, we have less than 256 solvers. Very few Project Euler members have been able to assemble the methods required to solve Project Euler 585. I guess the gradation of problems into levels means not every problem is appropriate for everyone at all times. Unless you have solved enough problems to gain the know-how, Problems like 585 might be out of reach. I like the fact that lot of effort was put into tags and the newer levels, but I still believe on the whole Project Euler works more as a "challenger" and much less of a "teacher" and this might lead to less active user participation. At the end of the day, Project Euler does kindle a desire to learn some mathematics and computing; but you don't want to run into walls (like Problem 585) too soon.

pleasant.timepass wrote: Mon Apr 27, 2026 7:42 pmAre you sure they all appreciate something as hard as Problem 585?

Trying to please everyone with every problem is never going to work, so this is a red herring.

Agreed, not everyone will be happy with every problem, but a utilitarian argument is to be made for the lower 99%.

Knowing that there are hard problems is very attractive.

A random research problem might be too hard to be solved for 1000s of years, making your efforts misguided. But here we have hard problems that are known to have a solution, which is a great tool to improve problem solving.

That was probably true ten years ago, now with the leaps and bounds in GenAI, how long before some GenAI company runs their GenAI tool on Project Euler problems as a marketing stunt?

EDIT:
I recently stumbled upon a website that contains not just solutions in three programming languages, but also mathematical explanations to all 1002 of Project Euler problems. As the Project Euler team itself seems to have reconciled themselves too: at some point either a GenAI or someone with access to a powerful GenAI might end up posting all Project Euler solutions online. Now the question is what to do about these resources available on the web? I for one, finally understood a technique to solve Problem 152 and with some help from GenAI solved the problem 152 in two different ways, both solutions are posted in the problem 152 discussion-thread under user "PleasantTimepass" (page 8, second post from the bottom). I am not sure whether by myself I would have been ever able to solve Problem 152, much less understand a technique to solve this problem. So, are we just copying the solution to a crossword or taking the time to understand the solution to the crossword!