Some Reflections on Solving Every Project Euler Problem

In which I overshare, probably

On July 31, 2025, I obtained the "Perfection" award on Project Euler. I had solved all 956 numbered problems. Since then one additional problem has appeared (usually one new problem is released per week, but Project Euler takes a break for a few weeks each summer), which I have also solved. According to the official statistics, I am, as of this writing, one of 11 people who have solved every problem currently available.

My History with Project Euler

One does not solve 957 Project Euler problems in a day, a week, a month, or even a year. Project Euler has been around since 2001; when I first found it, in late 2012, it already had over 400 problems. I used Project Euler as a way to do math while procrastinating on working on my doctoral thesis; by January of 2014 I had solved over 300 problems.

And then I dropped it for nearly four years.

I picked up Project Euler again in late 2017 when, having decided to leave academia for industry, I wanted a fun way to get back into programming. I solved around sixty problems in three months, and then, after securing a job offer and with way too many other priorities, I dropped it once again. Over the next five years I would pop back in and solve a few problems, mostly easy ones, every few months to a year. At the beginning of 2023 I had solved about 425 problems.

You would be forgiven for thinking that this was more than 50% progress toward what was, at the time, a total of about 820 problems released. In reality, the progress was something more like 20%. These 425 problems included not only the first 100 problems, most of which are much easier than almost any of the problems which follow, but of the other problems I'd solved, almost all were in the easier half of the remaining problems. And the difference between an easy and a hard Project Euler problem is vast, with the easiest problems accessible to bright middle school students or programmers with no particular mathematical talent, and the hardest problems difficult enough to challenge many IMO and IOI medalists for days or even weeks. Of the approximately 425 problems I had solved at the beginning of 2023, exactly two are problems currently rated among the 100 hardest on the site (and this is arguably two more than is accurate, as the internal difficulty ratings are generally considered to be inflated for problems from early in Project Euler's history).

And then, in spring of 2023, I decided to come back to Project Euler. In April, shortly after solving my 450th problem, I wrote a long explainer post about Project Euler for an internet forum, in which I said, of the people who had solved every then-published problem, that "that feat requires both remarkable intelligence and a frankly insane amount of dedication".

Well, Project Euler has been my primary hobby for the last two and a half years. I began attempting, and solving, some of the actual hardest problems on the site. Seven problems I contributed were published. And finally, at the end of July 2025, I had zero unsolved problems remaining. I'm not sure that I want to assert I have "remarkable intelligence", but I stand by my other claim: solving every problem requires an insane amount of dedication.

Growth in Confidence, Confidence in Growth

Solving difficult Project Euler problems requires many things. Raw intelligence and creativity. Broad mathematical knowledge. Skill in designing efficient algorithms. Instincts honed by solving many previous problems. All expected, more or less. But there's one other thing that's of paramount importance in solving these problems, and that is confidence in one's ability to do so.

It's easy to get intimidated by a hard problem. To read the description and have no idea where to even begin. To see the list of fastest solvers, and be frightened that fewer than twenty... or fewer than ten... of the extremely smart people who wait, with bated breath, for each new problem release, managed to solve the problem within twenty-four hours. To see that it took more than a week to reach fifty solvers, maybe more than a year to reach one-hundred. The hardest problems on Project Euler are scary.

But they are solvable. Unlike research problems, you can be sure of that, because others have solved them. I didn't give this enough credit early on. Solving the hardest problems seemed like an impossible accomplishment — a bit silly, in retrospect, for someone who'd been a USAMO winner and completed a PhD, but it was how I felt. Solving the 100%-rated problems (the highest difficulty rating on the site) was not for mere mortals, or so I thought.

At some point in 2023, a switch flipped. I solved my first 100%-rated problem, after about 12 hours of work over a weekend. Then another. And another. I solved what is currently rated the hardest problem on the site. On seeing a problem which I had no idea how to do, and having every indication of its being extremely difficult, I began to think not "I can't solve this problem," but "I can't solve this problem yet."

Completing Project Euler in the last couple years has been very healing for me, because it helped me regain my confidence in my ability to grow and learn. I've been burned out a lot ever since early in grad school, and I unhappily left math academia after giving up the pure research route and teaching at a SLAC for a few years, then got burned out doing software in industry as well. It was easy to look at my past accomplishments and say: "I guess I peaked early, and I can't really do things anymore." Well, however useless for my tech career Project Euler is, and however much it differs from the math research I really wanted to do with my academic career, solving all these hard problems in Project Euler is something.

Of course, in the real world not all problems can be solved. But going toe-to-toe with problems that challenged some of the most talented problem-solvers in the world, problems which seemed utterly impenetrable at first, and winning: well, maybe I can actually still do things after all. Maybe I will be able to do math research again, even if not as a professor. Maybe I can choose to sculpt my life the way I want to live it, and make it work, even if I'm not temperamentally suited to the normal expectations of an academic or tech career. Maybe my past burnout and current problems with sleep and health and so on don't have to mean I'll "never live up to my potential," as I so frequently would tell myself.

I'd be lying if I said things were now all sunshine and roses, of course. I've dealt with both physical and mental health issues throughout all this time. I've even gone into stupid funks because I failed to solve a newly released Project Euler problem suitably quickly. Sometimes I despair of actually getting my health and sleep in order enough to stay on top of all the things I need and want to be doing.

But, well, those problems are probably solvable too, even if I don't know how. Yet.

You were probably expecting something more math related

I plan on writing an in-depth guide to approaching Project Euler soon. I've got a bunch of thoughts, now that I've actually solved all the problems. For now, if you like math and programming (or even just if you like math and are so-so on programming), you should go do Project Euler. You'll be sure to find problems you can solve... and many more you can't solve. Yet.