## Some problem and user statistics

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LilStalker
Posts: 54
Joined: Thu Nov 03, 2016 4:32 pm

### Some problem and user statistics

Since the fastest solvers table for problem 650 was filled pretty quick (a little over 6 hours) I got an idea to redo some analysis on problems which I did as a project for some course at university 3 - 4 years ago. Anyway I hope you will find the statistics interesting. I definitely did.
I took fastest solvers table for all the problems that have this statistics available. This is available for all the problems past number 277. In total we have data for 374 problems. Most of the fastest solvers tables are filled up to 100 places but early on and in some problems in the 4 hundreds that is not the case.

Okay to the statistics. Lets first do the fastests:

Top 10 fastest first places

1. Problem 551 : Min_25 : Time needed : 1 minute
2. Problem 592 : Min_25 : Time needed : 2 minutes, 27 seconds
3. Problem 301 : rng_58 : Time needed : 2 minutes, 35 seconds
4. Problem 625 : Min_25 : Time needed : 2 minutes, 41 seconds
5. Problem 345 : Anton_Lunyov : Time needed : 2 minutes, 53 seconds
6. Problem 493 : Tepsi : Time needed : 3 minutes, 6 seconds
7. Problem 521 : Min_25 : Time needed : 3 minutes, 18 seconds
8. Problem 622 : Zach-Lurf : Time needed : 3 minutes, 25 seconds
9. Problem 638 : xudyh : Time needed : 3 minutes, 41 seconds
10. Problem 429 : xudyh : Time needed : 4 minutes, 14 seconds

Top 10 fastest 10th places

1. Problem 301 : time needed : 10 minutes, 4 seconds
2. Problem 504 : time needed : 10 minutes, 59 seconds
3. Problem 429 : time needed : 11 minutes, 37 seconds
4. Problem 357 : time needed : 14 minutes
5. Problem 549 : time needed : 14 minutes, 28 seconds
6. Problem 381 : time needed : 14 minutes, 58 seconds
7. Problem 491 : time needed : 15 minutes, 51 seconds
8. Problem 345 : time needed : 15 minutes, 55 seconds
9. Problem 493 : time needed : 17 minutes, 3 seconds
10. Problem 601 : time needed : 18 minutes, 17 seconds

Top 10 fastest 50th places

1. Problem 493 : time needed : 1 hour, 1 minute, 30 seconds
2. Problem 650 : time needed : 1 hour, 8 minutes, 19 seconds
3. Problem 504 : time needed : 1 hour, 24 minutes, 39 seconds
4. Problem 549 : time needed : 1 hour, 44 minutes, 15 seconds
5. Problem 622 : time needed : 1 hour, 53 minutes, 20 seconds
6. Problem 500 : time needed : 1 hour, 58 minutes, 31 seconds
7. Problem 630 : time needed : 2 hours, 42 seconds
8. Problem 609 : time needed : 2 hours, 7 minutes, 46 seconds
9. Problem 601 : time needed : 2 hours, 11 minutes, 5 seconds
10. Problem 643 : time needed : 2 hours, 20 minutes, 5 seconds

Top 10 fastest 100th places

1. Problem 549 : time needed : 5 hours, 30 minutes, 42 seconds
2. Problem 493 : time needed : 5 hours, 52 minutes, 28 seconds
3. Problem 650 : time needed : 6 hours, 16 minutes, 23 seconds
4. Problem 622 : time needed : 7 hours, 25 minutes, 45 seconds
5. Problem 587 : time needed : 8 hours, 10 minutes, 20 seconds
6. Problem 504 : time needed : 8 hours, 22 minutes, 12 seconds
7. Problem 500 : time needed : 8 hours, 34 minutes, 30 seconds
8. Problem 429 : time needed : 8 hours, 57 minutes, 53 seconds
9. Problem 491 : time needed : 10 hours, 12 minutes, 2 seconds
10. Problem 613 : time needed : 11 hours, 15 minutes, 8 seconds

As we can see the last problem 650 did pretty well in those statistics. This statistics can give us one 'measure' of how hard the problem is. Of course the time of the first place or 10th place might not be so relevant since the problem might be easy for veterans and will be quickly solved by them but for others it could be hard. However looking at fastest 50th place or fastest 100th place can definitely give us a good idea which of the problems were the 'easiest'.

As we can see problem 301 isnt seen in fastest 50th and 100th places since the fastest solvers table is only filled up to 20 places and there isn't data available up to 100th place. However I believe it would rank pretty high also.

Thing that needs to be considered is of course also the release time of the problem. Problem 650 had a pretty nice timing for almost everybody and that definitely is one of the factors why it got to 100 solvers so fast.

Okay which of the problems were the 'hardest' as in which problems took the most time to get X amount of solvers:

Top 10 slowest first places

1. Problem 328 : wrongrook : Time needed : 18 hours, 6 minutes, 45 seconds
2. Problem 453 : aleksey : Time needed : 12 hours, 24 minutes, 41 seconds
3. Problem 344 : Zink : Time needed : 11 hours, 3 minutes, 24 seconds
4. Problem 379 : glodavac : Time needed : 10 hours, 34 minutes, 30 seconds
5. Problem 566 : aleksey : Time needed : 9 hours, 47 minutes, 41 seconds
6. Problem 415 : uwi : Time needed : 5 hours, 31 minutes, 4 seconds
7. Problem 579 : aleksey : Time needed : 5 hours, 28 minutes, 53 seconds
8. Problem 433 : grechnik : Time needed : 5 hours, 28 minutes, 21 seconds
9. Problem 319 : x22 : Time needed : 4 hours, 56 minutes, 53 seconds
10. Problem 361 : andrewelveyprice : Time needed : 4 hours, 48 minutes, 12 seconds

Top 10 slowest 10th places

1. Problem 566 : time needed : 2 days, 19 hours, 39 minutes, 11 seconds
2. Problem 289 : time needed : 2 days, 3 hours, 46 minutes, 41 seconds
3. Problem 597 : time needed : 1 day, 21 hours, 31 minutes, 23 seconds
4. Problem 328 : time needed : 1 day, 16 hours, 7 minutes, 10 seconds
5. Problem 459 : time needed : 1 day, 9 hours, 48 minutes, 17 seconds
6. Problem 453 : time needed : 1 day, 8 hours, 47 minutes, 38 seconds
7. Problem 415 : time needed : 1 day, 7 hours, 59 minutes, 58 seconds
8. Problem 585 : time needed : 1 day, 6 hours, 22 minutes
9. Problem 344 : time needed : 1 day, 5 hours, 4 minutes, 29 seconds
10. Problem 427 : time needed : 1 day, 3 hours, 25 minutes, 4 seconds

Top 10 slowest 50th places

1. Problem 585 : time needed : 18 weeks, 1 day, 21 hours, 3 minutes, 46 seconds
2. Problem 597 : time needed : 13 weeks, 5 days, 8 hours, 5 minutes, 22 seconds
3. Problem 566 : time needed : 13 weeks, 4 days, 48 minutes, 46 seconds
4. Problem 450 : time needed : 11 weeks, 4 days, 12 hours, 16 minutes, 39 seconds
5. Problem 495 : time needed : 10 weeks, 1 day, 22 hours, 26 minutes, 5 seconds
6. Problem 579 : time needed : 10 weeks, 6 hours, 36 minutes, 10 seconds
7. Problem 415 : time needed : 8 weeks, 1 day, 3 hours, 47 minutes, 51 seconds
8. Problem 439 : time needed : 7 weeks, 6 days, 11 hours, 14 minutes, 49 seconds
9. Problem 459 : time needed : 7 weeks, 5 days, 2 hours, 51 minutes, 30 seconds
10. Problem 483 : time needed : 5 weeks, 6 days, 3 hours, 18 minutes, 2 seconds

Top 10 slowest 100th places

1. Problem 579 : time needed : 109 weeks, 15 hours, 20 minutes, 46 seconds
2. Problem 483 : time needed : 99 weeks, 5 days, 21 hours, 29 minutes, 25 seconds
3. Problem 585 : time needed : 99 weeks, 2 days, 2 hours, 10 minutes, 11 seconds
4. Problem 495 : time needed : 86 weeks, 1 day, 13 hours, 39 minutes, 20 seconds
5. Problem 597 : time needed : 81 weeks, 1 day, 23 hours, 30 seconds
6. Problem 478 : time needed : 75 weeks, 6 days, 21 hours, 8 minutes, 31 seconds
7. Problem 559 : time needed : 66 weeks, 3 days, 1 hour, 16 minutes, 59 seconds
8. Problem 494 : time needed : 62 weeks, 1 day, 9 hours, 15 minutes, 10 seconds
9. Problem 489 : time needed : 60 weeks, 5 days, 10 hours, 11 minutes, 2 seconds
10. Problem 584 : time needed : 54 weeks, 22 hours, 51 minutes, 8 seconds

Note that some of the problems might be missing from top 10 slowest 100th places since they still don't have 100 solvers. One of those problems is problem 566 which would be taking the 1st place.

One interesting thing I was thinking about doing and might do it later is check for problems that scored high in lets say fastest 50th places statistics and then scored really low in the fastest 100th places. This would identity the problems that weren't so hard for a minority, but for the persons not familiar with the topic to be super hard.

What I was also interested in was who are the best performing users on Project Euler. I decided to look at this by few interesting criteria.
- Most first places
- Most top3 places
- Most top10 places
- Most top50 places
- Most points scored (51 - place if the place was <= 50. Same scoring as in Best Eulerians)
- Average place (with the constraint that a person has to be in the fastest solvers table for atleast 10 different problems)

Top 10 by most first places

1. : Anton_Lunyov : 46
2. : Min_25 : 44
3. : uwi : 35
4. : aleksey : 26
5. : grechnik : 24
6. : rng_58 : 20
7. : x22 : 17
8. : xudyh : 14
9. : Nabb : 9
10. : wrongrook : 8

Top 10 by most top3 places

1. : Anton_Lunyov : 102
2. : aleksey : 85
3. : uwi : 81
4. : Min_25 : 80
5. : x22 : 76
6. : grechnik : 68
7. : xudyh : 30
8. : wrongrook : 29
9. : rng_58 : 25
10. : Tepsi : 25

Top 10 by most top10 places

1. : x22 : 251
2. : aleksey : 225
3. : Anton_Lunyov : 174
4. : uwi : 167
5. : Min_25 : 147
6. : grechnik : 130
7. : Tepsi : 102
8. : djdolls : 76
9. : cmk : 66
10. : Lucy_Hedgehog : 66

Top 10 by most top50 places

1. : x22 : 371
2. : aleksey : 357
3. : uwi : 335
4. : Tepsi : 294
5. : utomaya : 284
6. : cmk : 266
7. : grechnik : 229
8. : sergej.samborskij : 228
9. : Anton_Lunyov : 215
10. : djdolls : 203

As we can see there are some really talented users that have been part of Project Euler for a very long time (or still are). Of course the most wins statistics might be the most prestigous one. But there are interesting things to see in the most top50 places also. In total data of 374 problems was collected and in 371 of those problems user x22 took place 50 or lower. The only problems in which he did not make it to top50 are 412 (not in the table), 597 (55th place) and 626 (74th place).
Of course congratulations too all the other users in those tables also. They all have incredible stats.

For the end, lets check the best performers by last two criteria:

Top 10 by most points scored

1. : x22 : 15327
2. : aleksey : 14679
3. : uwi : 12562
4. : Tepsi : 9630
5. : Anton_Lunyov : 9441
6. : grechnik : 8817
7. : cmk : 8670
8. : Min_25 : 8529
9. : utomaya : 7460
10. : djdolls : 6811

As we can see, the names don't really change much.

Top 10 by average place (when on fastest solvers table)

1. Anton_Lunyov : 7.9954 - problems counted : 218
2. hirose : 8.6203 - problems counted : 79
3. rng_58 : 8.6452 - problems counted : 31
4. bjin : 9.1538 - problems counted : 13
5. niino : 9.5 - problems counted : 16
6. Nix9 : 9.9091 - problems counted : 11
7. x22 : 9.9839 - problems counted : 373
8. aleksey : 10.0894 - problems counted : 358
9. cgy4ever : 10.2593 - problems counted : 27
10. Min_25 : 10.5463 - problems counted : 205

I will end this post with the table of users that have the most top3 places but haven't yet managed to get the number 1 place.

1. : djdolls : 11
2. : cmk : 6
3. : DjinnKahn : 4
4. : DerekLedbetter : 4
5. : whzzt : 3
6. : utomaya : 3
7. : tokoharu : 3
8. : stqn : 3
9. : sergej.samborskij : 3
10. : int : 3

I hope you find this interesting. If you have any other idea of what kind of statistics it might be interesting to look at, please say so Also if you would like to see your statistics you can say so (you can also PM me).
Last edited by LilStalker on Sun Jan 13, 2019 6:48 pm, edited 1 time in total.

v6ph1
Posts: 114
Joined: Mon Aug 25, 2014 6:14 pm

### Re: Some problem and user statistics

What about the number of the best placements per person (ordered like in the olympic games)?
1. xyz (50 times 1st)
2. abc (26 times 1st)
...
19. dfg (40 times 2nd)
...

Many of these statistics are interesting - but they are only as half as interesting, if you can not find your self in it.
And I would prefer a best time statistic depending on the local time of the user. (I would expect that midday-problems are solved faster than midnight-problems)

Are there differences of the activity-profile per country?

Country depended best lists would be a great idea.

But I would look at these statistics too, if they are only visible at the statistics page of PE.

LilStalker
Posts: 54
Joined: Thu Nov 03, 2016 4:32 pm

### Re: Some problem and user statistics

Thank you for the ideas. I will soon try to check those too.

There are really many ways to look at those problems depending on what time (according to your local time) the problem was published and what the difficulty of the problem was.
I would guess that users are most effective for problems published in the afternoon or early in the evening. Yeah, It might be an interesting stat to look at (users split by country and considering their local time at the time of publish).

MHealy
Posts: 38
Joined: Sat Nov 17, 2012 11:32 pm

### Re: Some problem and user statistics

Yes, some very interesting statistics - thanks! Many very impressive scores, but I must say I was probably most surprised that somebody has managed to come top 50 in all but three of the tracked problems. Congratulations x22!

One small thing: I think this must be a typo?
I will end this post with the table of users that have the most top10 places but haven't yet managed to get the number 1 place.
Because otherwise some numbers in this list contradict total number of top 10 finishes in the other one.

A statistic I think would be nice is max Eulerians score (i.e. highest sum of points from 5 best top 50 finishes in any 10 contiguous problems). I think I'm aware of four users achieving the maximum "250/250" score, but I'd be interested to see if there are others, and also how far down this list I am! It would help control a little for newer or less active users (eg. mnbvmar recently got to 250/250 but is nowhere on these tables).

LilStalker
Posts: 54
Joined: Thu Nov 03, 2016 4:32 pm

### Re: Some problem and user statistics

Yep It was a typo. The table was for the users with most top3 finishes but without ever managing to take the number 1

Here is the table for most top10 finishes without ever getting the gold medal:

1. : djdolls : 76
2. : cmk : 66
3. : umu : 46
4. : DerekLedbetter : 40
5. : sergej.samborskij : 35
6. : Bobbit : 30
7. : utomaya : 28
8. : WG4ZHZ2P2Q : 25
9. : tokoharu : 21
10. : DjinnKahn : 18

Also I think it is a great idea to implement max Eulerian score. Will do that!