Difficulty Levels & Awards Update (January 2026)

[cryptic_penguin]

TL;DR suggestion: Only change the difficulty settings at a set time once per week.

Perfecting Difficulties Award:

I agree with Arxyj (above): The unstability of the difficulty setting is annoying. On an almost daily basis my level for the “Perfecting Difficulties“ award shifts between 25 to 27 (of 28). Last night it was at 27, so I set out trying to solve the ‘missing’ problem. Almost made it, but had to go to bed. This morning the difficulty ratings have had yet an earthquake and I am now at 25 of 28, and the almost-solved problem is no longe a missing difficulty. Getting the award as a result of yet an earthquake will also be less satisfying. Only changing the difficulty settings at a fixed and announced time for instance once per week would help a lot. As of now it is annoying to be so near and have had the award moved away literally overnight.

I really like the idea of this suggestion. I do quite like the new difficulty system quite a lot, but the shifting around is the one thing which I hate, and it can be extremely frustrating when I put in hours of work to solve a problem at a new difficulty level, only for it to move down to one I've already solved a problem at the next day - something which has now happened to me on multiple occasions.

The thing is, the uncertainty measure doesn't really help because for all the problems around difficulty level 20, they all have a red uncertainty bar, and they shift multiple places sometimes - for instance, a few weeks ago, problem 147 was rated a 21, but is now a 24.

For someone like myself who is just alright at maths and has to spend a lot of time researching and thinking to solve some of the middle-difficulty problems (when I'm able to), but also wants to get as many achievements as I can, I really do not like this one flaw.

[euler]

Using a weekly update would not help. In fact, it could make it worse as the observed jumps might be potentially more severe. Although, the jumps are definitely becoming less and less.

The issue we have is that the new system is relatively new compared to the life of Project Euler and it is still learning about the difficulty levels of each problem. Due to the visibility of some problems (i.e. hiding away in page X/20) the system has less knowledge of some and so one of those rarer solves can cause that problem to move more than others. And even as each problem becomes better known by the system, the movement of other problems around it is what can cause a well-established problem to apparently move. This is the price we pay for a superior system that allows a dynamic difficulty measure.

As this system has been developed, and since long before its public release, I was monitoring the stability. Prior to release we were satisfied that it was getting most problems spot on, but we knew there would continue to be shifts here and there, albeit with decreasing frequency. I can assure you that the vast majority of problems are really beginning to settle. I am planning to add a new statistics page when I get the time that will show the min/max levels of problems over a period of time. To give you some idea, looking at the minimum and maximum levels for each problem over the past two weeks for problems 1-977, this is the frequency of level changes:

Code: Select all

DeltaL	Count
0	625
1	320
2	28
3	3
4	1

In fact, with reference to the unique difficulty level awards, you are almost just as likely to be gifted a previously unsolved level as you are to be robbed of one. Although in theory the "perfecting difficulties" can be earned by solving the minimum of just 28 problems, for your own satisfaction of knowing that you have truly begun to master a large number of difficulty level, you really want to be in the position that you have solved at least a couple of problems at each level. If you're still determined to get it based on the minimum number of problems, then I would recommend sorting on difficulty levels and targetting those in the middle of a level. The problems that are close to the level above or below are those more likely to switch between adjacent levels.

I understand the frustration for achievement hunters and I certainly hope that award doesn't become so frustratingly difficult to obtain that we need to remove it completely. Although some members like to target particular awards, the purpose of them is that little surprise once in a while when an unexpected notification pops up that you've done something a little bit special. I would say, be patient, and just continue to enjoy solving the problems. As always, I will never stop monitoring the situation and considering alternatives that provide a better experience for our members.

[TitanCode]

Using a weekly update would not help.

Yes, it would.

Twice during the last three weeks this has happened to me: I discover, I have solved 27 different levels, and start solving the 28th. When I finish solving, something else has been shifted. Last time it shifted all the way down from 27 levels to 24 levels in a single night. If I have had a full week to solve the ‘missing’ problem, I would have completed the award requirement.

It *feels* like every problem I solve gets moved down a level very soon after. But maybe that is what is happening: The system notice that problem X has been solved by a nobody with a low Elo rating, and bumps the level down a notch?

I very much value the work you Administrators and problem designers are doing here. I love that the Internet still have small, peaceful pockets for people who like to think deeply. The shifting difficulties are a just a small annoyance. I am just trying to suggest how to make the problem less frustrating, and I think only updating weekly and at a fixed time would help. The award it not so frustrating that I rather be without.

[euler]

[edit]When I said weekly updates wouldn't help, I wasn't referring to your particular situation as an achievement hunter. Rather I was thinking about the bigger picture of how it would look to members. Seeing potentially large jumps each week rather than incremental changes on a daily basis might be more jarring. But more importantly, awards don't drive decisions that impact the public data, they exist as a secondary motivator. Which is why I said, if the data hasn't yet reached a point of being stable enough for people to set a realistic target, we might need to scrap that particular award.[/edit]

What problems have you been working on and when was it you saw a problem shift three levels? I'll have a closer look at its encounters to figure out if something is broken because it should be near impossible for a single problem to shift that far in one day.

I also wonder if this happened quite some time ago? Just over a week ago some background changes have been made that should cause the vast majority of problems to become even more stable.

[TitanCode]

When I mouse over ”Perfecting Difficulties” I now see
”… Progress: 25 / 28”

During one night I went from 27 /28 (i.e. only missing one) to 24 /28.

I don’t know then the shift from 27 to 24 last happened for me. Around the 24th, I guess.

[TitanCode]

shift three levels?

I don't know if this is interesting: Problem 170 (Pandigital Concatenating Products) has climbed down two levels. Was level 27 on Marts 16th. Today it is level 25.

[euler]

This is to do with problem visibility and having a rank teetering around a multiple of 25. Here is the data (showing rank and level) for problem 170 from 15 March to last night; the data is captured daily at 1am UTC just before the ranks update, so the date actually represents the rankings from the previous day.

Code: Select all

2026-03-15	2026-03-16	2026-03-17	2026-03-18	2026-03-19	2026-03-20	2026-03-21	2026-03-22	2026-03-23	2026-03-24	2026-03-25	2026-03-26	2026-03-27	2026-03-28	2026-03-29	2026-03-30	2026-03-31	2026-04-01	2026-04-02	2026-04-03	2026-04-04	2026-04-05	2026-04-06	2026-04-07	2026-04-08	2026-04-09					
684	27	686	27	689	27	686	27	683	27	683	27	683	27	669	26	675	26	663	26	664	26	661	26	652	26	653	26	655	26	654	26	654	26	658	26	648	25	650	25	652	26	655	26	645	25	646	25	646	25	648	25

The first part of its journey is settling to its proper place and then from the data you can see it seems to be around the top of level 25 to the bottom of level 26.

I am hoping to have that kind of data available for all problems, but until we can be sure we have the right system in place it'll have to wait. We are currently working on a tweak to the system that should help to ground the data, but if we do go down that route it will unfortunately cause sudden changes to a number of problems. It depends on whether or not this is going to be worth the trouble: the inevitable upset caused by the annoyance of yet another change versus us trying to what is ultimately the best for our members by providing the most meaningful data possible. The biggest upset would be those, like you, working on problems based on difficulty to have the rug pulled out from under your feet again.

[TitanCode]

I rather have a few sudden changes and long periods of stability. Knowing date and time also is helpful. But the most important thing is that the difficulty levels are as true as possible (whatever that means....) The old 5% rating of Eulercoin Problem 700 (now level 15) was also frustrating.

Whatever you decide: Thank you for the work you put into the site. I am having fun, so much that I picked up a math book “Journey through Genius: The Great Theorems of Mathematics” by William Dunham.

[euler]

That book is an absolute treasure and William Dunham is a delight to read. His "The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities" is very good too, but I'd especially recommend "Euler: The Master of Us All" if you want to get an overview of the true genius of Euler.

[TitanCode]

an overview of the true genius of Euler.

says ..... Euler

[TitanCode]

Seems to work as intended:
One of the nightly updates have lead to me having solved 28 different levels, and I received the award. Another update lead me back to having solved only 27 levels. The award stayed.

[euler]

Good to know. Obviously the award will remain intact, but it'll be interesting to see how your solve distribution per level looks for you later today when I do the update to the ranking algorithm.
See Update to the Ranking Algorithm

[TitanCode]

Funny thing is that I jumped from having 27 levels solved to 29 levels.

I also noticed that Eulercoin (problem 700) has had quite a journey. In the old system it was 5%. I was happy to see it jump to level 20 when the new system was introduced (guess who hasn’t been able to solved it....) Now it has landed on 8 (22%).

Problem 893 Matchsticks dropped from level 19 to 9 (I agree with that one).

[i707107]

About High Five,

I am aware that the previous High Five definition is
"Solve the five most recent problems"

Now, in thw Awards, I see that the definition became
"Solve the five recent problems"
where "recent problems" can be any of the last 10 problems.

But, I think the real criteria still obeys the previous definition.

Would it be possible that either change the definition to match the real criteria, or change the real criteria to match with the current definition?

[euler]

The new description had become, "Solve five recent problems". But you were right, it was only checking the most recent five (the previous criteria). I've changed the criteria to match the new description. You can solve any of the five most recent problems now to unlock it.

[QuasiRus]

Hello, I do not understand how "Dating Game" award works, which timezone is taken into account? I submitted two problems (78 and 66) at 28th 01:51 and 02:09 by my local time, but none is counted, 28th is still missing...

[euler]

The script was using the solve date which is stored in the DB as UTC, so I have modified it to retrieve your time zone and apply that to the check. If you visit your awards page, it always rechecks your existing awards. So could you visit it now to see if it unlocks?

[QuasiRus]

So could you visit it now to see if it unlocks

Yes, now I see it is unlocked! Thank you!