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Cain's Jawbone: Puzzle solved for just third time in almost 100 years (2020) (theguardian.com)
158 points by mmettler on Jan 17, 2022 | hide | past | favorite | 57 comments



Past related posts:

Beastly Clues: T. S. Eliot, Torquemada, and the Modernist Crossword - https://news.ycombinator.com/item?id=29911071 - Jan 2022 (3 comments)

Literary puzzle solved for just third time in almost 100 years - https://www.theguardian.com/books/2020/nov/10/literary-puzzl... (via https://news.ycombinator.com/item?id=25045947 - Nov 2020, but no comments there)

Edit: maybe we'll switch to that latter article from https://en.wikipedia.org/wiki/Cain%27s_Jawbone. Wikipedia pages are fine when the topic is unpredictable (like this one!) and there isn't a good third-party article available (https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...).


Here are some pictures of some pages:

p.15: https://i.imgur.com/xKRESSL.jpg

p.23: https://i.imgur.com/ODDenKQ.jpg

p.93: https://i.imgur.com/0vAvWYt.jpg

I suspect page 23 continues onto page 93, but that's about as easy as this puzzle ever gets. Each page begins and ends in whole statements and there's not, for example, any dialogue split between pages. The occasional poem fragment is the only easy clue you get.

The rest of it likely requires paying attention to the subject(s) and setting on each page and gradually assembling them. I have no expectation of ever solving it, and if I ever do get the pages into some kind of order, I doubt I'll be completely confident about my answer.

Some kind of NN model could probably be constructed that would do a pretty good job of getting it mostly in order. Somebody else might find that to be a fun problem, but I picked it up for its potential to be a long-term amusement.


What about page 41 before 93 instead of 23? The poem fragment is actually the previous part of that poem. (https://www.poetryloverspage.com/poets/kipling/mary_gloster....).

Although the rest of the text outside the poem seems to match less...

I imagine piecing together these literary references would have been much harder in the 30s compared to now where you can just google them, and ctrl-f the whole text of the book.


Ah, you're right, and 23 continues onto 87. I was going off of rhyme and meter, and hadn't yet looked them up.


Aren't the big GPT models really good at knowing what comes next? Could they be used to instead score what the most likely next sentence is given a list of 99 choices? Given that, should be trivial to scan the 100 pages, OCR them, feed them to this ranking system, then order them based on the scoring metric.


> Aren't the big GPT models really good at knowing what comes next?

Good at coming up with something that COULD come next and sound reasonable but the possible directions the story could go after each page is infinite.

The storyline is likely to be vastly different from the 'real' story let alone the actual wording. See these alternate endings for Game of Thrones:

https://towardsdatascience.com/openai-gpt-2-writes-alternate...


It's a generative model (in the mathy sense) so you can take any page and look at the model's probabilities of the first sentence from each of the other 99 pages. This should give some strong hints at least.


This reads like Ulysses, or what I imagine that book to read like.


The article talks about the number of possible page combinations as if it's a meaningful indicator of difficulty, but I don't think it really is unless you're actually trying to brute force the solution.

If you aren't just brute forcing it then the difficulty depends much more on the clues given to you in the book. (For a trivial example imagine if the pages were numbered - technically still roughly 10^157 possibilities, but it would be very easy to solve).


>The article talks about the number of possible page combinations as if it's a meaningful indicator of difficulty, but I don't think it really is unless you're actually trying to brute force the solution.

Yep, my first thought is the Rubik's Cube. Pretty much any scramble is equally easy to solve when applying one of the common solving methods, so the ridiculously high number of possible permutations doesn't matter at all in practice.

The fact that the white-green edge can start in 12 different spots doesn't matter when you just look for that piece and then move it into place. You take it all a step at a time. A "hard scramble" will barely affect solve time by a few seconds at most.

Having the piece in the right spot but rotated the wrong way is about as hard as you can make it, since then you have to "take it out" and "reinsert it" the other way versus just inserting it from elsewhere the proper orientation right away.


> the ridiculously high number of possible permutations doesn't matter at all in practice.

I'm not sure I'd go that far. For the most part, the difficulty level of twisty puzzles does tend to increase with the number of possible permutations. The big things I can think of that break up that tendency are jumbling and bandages.

It's just that the number of permutations doesn't give you a good intuitive sense of how difficult a puzzle might be.


Not just that, but you also have to provide other details to solve the puzzle:

https://en.m.wikipedia.org/wiki/Cain's_Jawbone

> The prize of £1,000 (roughly how much £15 was worth in 1934) will be given to the first reader to provide the names of the murderers and the murdered, the correct order of the pages and a short explanation of how the solution was obtained.


Quantitatively, for each pair of pages that you assume are in a certain order the number of admissible permutations is approximately halved: hopefully enough to go from 100! to a set of meaningful alternatives.


> technically still roughly 10^157 possibilities

And they say dynamic programming has no real world applications.


Possibly the first time I've ever laughed out loud at something in the Guardian:

"“The first time I opened the box, I swiftly concluded that it was way out of my league, and the only way I’d even have a shot at it was if I were for some bizarre reason trapped in my own home for months on end, with nowhere to go and no one to see. Unfortunately, the universe heard me,” Finnemore said."


I wonder how a modern language model would fare here -- use something like GPT-3 to evaluate the log likelihood gain of stitching together each of all N^2 possible pairs, then merge greedily best matches until none are left. Totally within reach, I bet it could get at least _some_ of the order right.


“The first time I opened the box, I swiftly concluded that it was way out of my league, and the only way I’d even have a shot at it was if I were for some bizarre reason trapped in my own home for months on end, with nowhere to go and no one to see. Unfortunately, the universe heard me,”

Finally it's working for someone!


Huh, I was sure the universe had heard me say I really didn't want to go the 2 (yes 2, not 1, not 0) meat raffles with my hated relatives the weekend everything got shutdown. What the hell is a meat raffle anyway?


If you hate these relatives why don’t you just… not go?


Probably because there are loved relatives who would be upset if OP didn't go.


I’ve heard the dating scene referred to as a meat market. Maybe they are raffling off the opportunity to go on dates with people? Otherwise… why would anyone raffle off real organic meat?



I... kinda want it? A decent cut of meat is expensive over here - to the point where I'm sure at least half of what a butcher's or grocery shop has out on display is discarded. The only affordable stuff is processed stuff like sausages and ground meat.

I mean part of me gets it, some meat (e.g. chicken) was getting too cheap - the €3,- a kilo chicken stunts caused a big outrage - and 'we' need to reduce meat consumption. But at the same time, meat is an essential part of a balanced diet - vegetarianism and veganism may be alternatives, but they need a lot more effort and headspace to make balanced, especially concerning vitamins, proteins, minerals, fats etc easily found in meat.


This is pretty common in New Zealand/Australia too. Although more so in the older generation I think.


I guess it sounds strange to an American, but they are still popular in smaller towns in Australia. The local businesses eg butcher or bottle shop will donate/provide at cost goods(meat tray/wine) to be raffled to raise funds for some local cause or sporting team.

The supermarket duopoly here has been killing off independant butchers so I suppose the classic meat raffle will gradually disappear too.


Our company has a meat tray (or vegan tray, or whatever most suits the winner) for our company trivia/friday fun points winner


its also a thing in Canada (am Canadian)


FTA:

- Just two readers managed to solve the puzzle in the 1930s

- three years ago […] Shandy Hall curator Patrick Wildgust embarked on a mission to solve it. Once he did

- John Finnemore […] was […] the only one to get the answer right.

⇒ at least the fourth time.


I think the implication is the first two people worked together, so they only count as one time.


I thought the implication was that Wildgust had not solved the puzzle, but rather found the author's answer through research.


>Wildgust confirmed that Finnemore’s solution was correct. He himself set out to solve Cain’s Jawbone first by typing out the entire novel, making a note of every literary reference he could find. This didn’t work. Then he searched libraries for copies of the book to see if any contained markings to help him. None did, but eventually he managed to find the answer.

>“Tracking down the correct solution for Cain’s Jawbone was a risky venture, and one peppered with possible pitfalls,” said Wildgust. “I can say no more on the subject, but eventually I was satisfied we were in possession of the correct solution.

Yes, I took this to mean he was looking for an answer key somewhere, and eventually found it.


After studying this discussion it seems that the puzzle has been solved several more times: There is an active subreddit dedicated to it [1], with a handful of people credibly claiming to have solved the puzzle.

So "solved for just the third time" is likely not technically true, but the puzzle does seem to be very very difficult.

[1] https://www.reddit.com/r/CainsJawbone/

(You can even find a digital version there, but it's not clear if clues have been lost in the digitalisation process).


Anyone know a place to buy a copy of the puzzle, either from Unbound or elsewhere?


I purchased two copies a few weeks ago from Unbound here: https://unbound.com/books/cains-jawbone-paperback/

It shipped from overseas and, as usual, was stuck in US Customs for about a week, but this was in the run-up to the holidays. Might be faster now.


Woah! It was listed as “sold out” on the Unbound website only hours ago. Thanks!


amazon.com claims to have it, although only as a paperback, not as the nicer collection of loose pages.


Amazon should print the book in the correct order.


When Black Mirror's Bandersnatch came out, I had it added on Plex. I watched it before I knew the concept behind it. All of the multiple storylines were played sequentially. I remember thinking, wow, way too avant-garde for me. It was only later that I realized that Netflix had an interface built around it for picking the storylines.


Slightly off topic, but if you get a chance then John Finnemore's radio work is amazing. Have a look for Cabin Pressure, John Finnemore's Souvenir Programme and Double Acts. He is a very talented comedian and story teller, and apparently somewhat of a polymath.


Cabin Pressure is Benedict Cumberpatch's finest work.


Well, that was an easy impulse buy. I ordered it from Amazon to be delivered in a couple of weeks.


For anyone else, found 3 version in this thread:

https://www.reddit.com/r/CainsJawbone/comments/qkiog1/free_d...

Docs, Slides and PDF.


Is that legal? I'm not moralizing, I just didn't see anyone address it. Can't remember how long ago it was originally published (although if the scans are from the more recent version, that probably doesn't matter).


I've never heard of this book before! That's such a cool idea, to have the pages out of order.


100! page ordering combinations is roughly 10^157 possibilities.


Yes there are 10^157 possibilities but I suspect it's not a factorial process to solve it - let's pick a random page, we compare it with the 99 others and find the one that follows it and the one that precedes it (198 tests) - now we have a chunk of 3 lets do the same again (194 tests) now we have a chunk of 5 (190 tests)

The result is more like 2*(99+98+97+....+1) tests which is ~10,000 tests something a person can do in a real amount of time - nothing like a 10^157 age of the universe sort of thing.

(of course there are going to be some pages that might have multiple potential subsequent pages - sentences that scan and make sense - so as there's more of a puzzle in there)


While some of the pages end in a poem fragment that can be plausibly matched to a poem fragment at the beginning of another page, none of the pages have obvious continuations to other pages. Each page starts at a whole sentence and ends at a whole sentence, and I haven't spotted any obvious hints, like dialogue spanning more than a page.

At the moment my plan is to cut the book up, glue a lightweight magnet to each one, get a couple of large magnetic whiteboards, and just stare at and rearrange them every now and again for the rest of my life.


Since people have apparently submitted attempts that were incorrect, it seems likely that it’s not at all easy to verify whether any pair of pages is correct.


The article actually points this out in a different wording at the beginning:

> The number of possible combinations is a figure with 158 digits


My first thought would be to find all the pages that begin a new sentence and/or finish with a completed one.


A good idea, but unfortunately the author has thought of that - every page starts and ends with a complete sentence!


i wonder if it can be brute-forced...


I doubt it, considering people have apparently submitted attempts which were unsuccessful. Assuming at least some of those were from fairly serious puzzle fans giving it a serious attempt, it’s probably not a puzzle where the solution is easily verifiable.


Well mostly I guess that the first part has to do with checking that the end of one page matches the beginning of the next, and makes sense (the "makes sense" bit probably can't be brute forced) - 100! is probably not easily brute forceable either - but I suspect that this is really a process something that might not actually be strictly factorial in nature.

But once you've done that I think there's an actual mystery to solve as well - probably something that requires an actual human to read it


I'm getting roughly 10^128 times the age of the universe at 1 trillion unique orderings checked per second. Still a chance though ;).


so an pi 4 should do it then.. ;)


given that the solution oracle is an actual human being, he might not be willing to yes/no that many proposed solutions.




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