Posted 6th Mar 2020 at 09:51Why do we have a Slitherlink every other day?:)

Posted 6th Mar 2020 at 22:48You are right for March so far - but before that I guess it averages out for every 3rd day (since the lost puzzle types came back).
Anyway. Another reason might be that the last Odd Pair was on Feb 25th. That's overdue.

If I understood correctly what gareth mentioned recently, there is a randomizer installed picking the puzzles. I guess dependant on the supply of a certain puzzle type that randomizer puts in some kinds more often than others. Slitherlinks come in three different sizes. Maybe the randomizer considers each size an own type, then it shows up as often as different sizes of other puzzle types (like 6x6, 8x8 and 10x10). On the other hand, bigger Sudoku sizes (12x12 or even 16x16) are really rare...

At least there seems to be the rule that a puzzle type doesn't repeat the next day (unless a Wraparound puzzle ends up being renamed making it two Jigsaws in a row...). If there were enough puzzle types, this rule could, indeed, be spread out to "no repeat the next two days". The list of puzzle types in the filter shows 20 different entries. That seems to be enough for a rule like "can not repeat for the next 3 or even 4 days". But then some people might ask for Jigsaw Puzzles show up more often than that.

But you are right: Slitherlinks seem to show up more often than most other types.

Posted 7th Mar 2020 at 01:37Sometimes I add puzzles manually. Beyond that, each class of puzzle has its own likelihood of appearing which varies from type to type. Then, if that class is selected, there is set of likelihoods for each of the types within that class. Slitherlink is just its own class, however, not distinguished by size. The only further complexity is that the same class doesn't appear two days in a row, as JoergWaysW says.

There are 20 puzzle classes, but the probability of a slitherlink appearing in an given slot is just less than 1 in 20 since every class has a different weight. But there are 4 slots to fill, and classes in slots the previous days are discounted. If we take out the previous day it's then on average a chance of about 1 in 16, so with 4 slots that means there is a roughly 25% chance of a slitherlink appearing on a day.

The actual appearance rate has been about 35% over the past year, but that was influenced by lots of missing puzzle types.

Posted 7th Mar 2020 at 12:05gareth, thank you for explaining all this.

I guess the Slitherlink weight is higher than the hitori one.

One question again:
Is Odd Pair Sudoku on the current list of missing puzzle Types?

Now some mathematical thoughts:

11 days without it - what would be the statistic chance of that?
If the Odd Pair class was average weighted with 5% chance of being picked, a non appearence for 11 days (44 Puzzles) had a probability of BINOMIAL(44, 0.05, 0) = 10.5% - higher than I thought.

Result: An average puzzle class in average is missing for 11 consecutive days once every three months (=about four times a year).

Same calculation gives a probability of the some average puzzle class showing at least 4 times in 11 days is at about BINOMIAL (44,0.05, 4.......44) = 17.6% - but this calculation doesn't include the no-repeat on the next day rule. When the puzzle is picked, it can not be picked again the same day or the next day -> in average it cannot be picked the next 6 times. If I assume it was picked at least 4 times that means it is not 44 times, but only 44-24 = 20 times possible to be picked again. Then I end up with BINOMIAL(20,0.05, 4......20) = 1.5% as probability for the same puzzle 4 times within 11 days. This is pretty low but also statistically not correctly calculated. That would probably require a complete tree graph.

Finally, I assume that Slitherlink is weighted higher than 1/20.
(1/20 means at a puzzle rate of 4 per day, that a puzzle class should come up once every 5 days in average)
In 13 years (since 2007?) you have 13*365*4=18980 daily puzzles, current Slitherlink has number 1619, that is a percentage of 8.5%>5%. The percentage would be higher if Slitherlinks or daily puzzles in general started later than 2007.

Note: I don't dislike Slitherlinks at all. I'm fine with it.

Posted 7th Mar 2020 at 13:06I don't like slitherlinks at all - not complaining, just saying, but there do seem to be a lot of them

Posted 7th Mar 2020 at 17:33
Last edited by Elisabeth 7th Mar 2020 at 17:37Nor do I Penelope but I seem to have started JWW off!!! Obviously we don't all like all the puzzles but hope 3 out of the 4 each day are acceptable:)

Posted 7th Mar 2020 at 17:35I say let's have more Slitherlinks and NO Hitoris - the latter are awful !
But it's all a matter of taste, of course.

Posted 8th Mar 2020 at 00:36A lot of the puzzle types didn't appear early on, so one reason slitherlink has appeared so many times is because it provides a very different type of challenge to the many sudoku variants - even more so when there were fewer other types of puzzle.

Here's some stats for the longstanding daily puzzles:
* 1621 slitherlinks have appeared, the first on 8th December 2007
* 2011 regular sudoku have appeared (non-variants), the first on 3rd April 2007
* 1980 kakuro have appeared, the first on 20th April 2007
* 779 hanjie have appeared, the first on 29th November 2007

A few other non-sudoku types:
* 871 hitori, the first on 18th March 2008
* 756 skyscrapers, the first on 15th March 2011
* 139 nurikabe, the first on 17th May 2012

Probability weights for the puzzles discussed in this comment thread plus a few more: (higher = more likely; linear scaling)
* Jigsaw sudoku = 5
* Sudoku = 10
* Killer sudoku = 10
* Nurikabe = 10
* Hitori = 10
* Calcudoku = 12
* Kakuro = 20
* Slitherlink = 25

So there we go. :) Total probability weight is 202, so slitherlink is actually more likely than I wrote above - I thought its weight was 20 but it is in fact 25.

Gareth, puzzlemix

Posted 8th Mar 2020 at 00:41And then to give an example of sub-type weights, here's the breakdown for the chances of different minor variants if sudoku is chosen:
* 6x6 = 2
* 8x8 = 2
* 9x9 = 20
* 10x10 = 2
* 12x12 = 2
* 16x16 = 1

Oh, and no, re the query above - odd pair sudoku is not missing and is in the rotation. The only type currently missing is the Mystery Calcudoku (Non-zero) subtype of Calcudoku.

Gareth, puzzlemix

Posted 8th Mar 2020 at 09:57I'm glad to see that Elisabeth was right.

I like to suggest, if I'm allowed to, to increase Jigsaw and to decrease Slitherlink - Slitherlink even seems to have the top weight! Nurikabe, Hitori, Hanjie and somewhat Skyscraper added to the "different type of challenge" pool after Slitherlink was introduced (and Kakuro is also part of the different kind of challenge variety).
My assumption is, that Slitherlink had to have a high weight at the beginning, like Kakuro, to balance against all the different Sudoku types (needed to have a mix that you can call a mix). But with added more variety later it could have been lowered over time.

I guess the total weight of 202 includes 100 more scores of weight that were not mentioned (the sum of the given scores is 102).

Overall it appears to be a well weighted mix (Slitherlink and Jigsaw should be reconsidered).

Gareth, thank you again for this great webpage, for the transparency of background information and for listening to the community.

Posted 8th Mar 2020 at 11:30Thank you for this discussion Gareth and JoergWausW. Much of it goes over my head, I never was keen on Stats and even more so now(!!!) and thank you JWW for saying I was right in my surmise than Slitherlink seemed to be coming rather too often!
It is good to be able to have these exchanges, thank you Gareth, even if I'm just in it for the fun these days:)

Posted 16th Mar 2020 at 23:42By the way, just to add to the above, jigsaw appears low because there are other very similar types that effectively add to the weighting, such as wraparound.

Posted 17th Mar 2020 at 21:12I thought wraparound was included with the toroidals, not jigsaws

Posted 17th Mar 2020 at 22:20Which is my point :)