The Lemon Fool

One of the world’s most fiendish literary puzzles – a murder mystery in which all the pages are out of order – has been solved for just the third time in almost a century.

British comedy writer John Finnemore has solved Cain’s Jawbone, a murder mystery that has 32m possible combinations

Cain’s Jawbone was dreamed up by the Observer’s first cryptic crossword inventor, Edward Powys Mathers, who was known as Torquemada. First published in 1934, it invites the reader to reorder the book’s 100 pages – there are more than 32m possible combinations – and solve the murders within.

...“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.

- https://www.theguardian.com/books/2020/ ... ns-jawbone

BobbyD wrote:

One of the world’s most fiendish literary puzzles – a murder mystery in which all the pages are out of order – has been solved for just the third time in almost a century.

British comedy writer John Finnemore has solved Cain’s Jawbone, a murder mystery that has 32m possible combinations

Cain’s Jawbone was dreamed up by the Observer’s first cryptic crossword inventor, Edward Powys Mathers, who was known as Torquemada. First published in 1934, it invites the reader to reorder the book’s 100 pages – there are more than 32m possible combinations – and solve the murders within.

...“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.

- https://www.theguardian.com/books/2020/ ... ns-jawbone

An extra puzzle is where the number 32 million comes from - the number of ways to order 100 pages is 100! = ~9.33262 * 10^157, so while the statement "there are more than 32m possible combinations" is correct, the earlier statement that it "has 32m possible combinations" is hugely off the mark!

It's conceivable that there are enough easy constraints (e.g. along 'page N cannot possibly follow page M because a sentence that's split between the two makes no sense whatsoever' lines) to reduce the 100! combinations to just 32m combinations that are at all plausible. But I cannot help thinking that it's even more plausible that somewhere along the line, someone simply dreamt up a number that the general populace would consider impressively big... (And if I had to guess where along the line, the original publication date of 1934 seems plausible - inflation and the development of computers since then has probably grown the proportion of the population that regards 32 million as not all that big a number a bit too much, so I would expect a modern-day dreamt-up number to involve billions or even trillions instead of mere millions...)

Gengulphus

Gengulphus wrote:

BobbyD wrote:

One of the world’s most fiendish literary puzzles – a murder mystery in which all the pages are out of order – has been solved for just the third time in almost a century.

British comedy writer John Finnemore has solved Cain’s Jawbone, a murder mystery that has 32m possible combinations

Cain’s Jawbone was dreamed up by the Observer’s first cryptic crossword inventor, Edward Powys Mathers, who was known as Torquemada. First published in 1934, it invites the reader to reorder the book’s 100 pages – there are more than 32m possible combinations – and solve the murders within.

...“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.

- https://www.theguardian.com/books/2020/ ... ns-jawbone

An extra puzzle is where the number 32 million comes from - the number of ways to order 100 pages is 100! = ~9.33262 * 10^157, so while the statement "there are more than 32m possible combinations" is correct, the earlier statement that it "has 32m possible combinations" is hugely off the mark!

It's conceivable that there are enough easy constraints (e.g. along 'page N cannot possibly follow page M because a sentence that's split between the two makes no sense whatsoever' lines) to reduce the 100! combinations to just 32m combinations that are at all plausible. But I cannot help thinking that it's even more plausible that somewhere along the line, someone simply dreamt up a number that the general populace would consider impressively big... (And if I had to guess where along the line, the original publication date of 1934 seems plausible - inflation and the development of computers since then has probably grown the proportion of the population that regards 32 million as not all that big a number a bit too much, so I would expect a modern-day dreamt-up number to involve billions or even trillions instead of mere millions...)

Gengulphus

Yes, a familiarity with the number of permutations available with a simple set of playing cards lead me to bump on that, but I felt the quote was worth leaving it uncommented on.

As to the confusion between 32m and more than 32m, well it was in the Guardian.

Gengulphus wrote:An extra puzzle is where the number 32 million comes from - the number of ways to order 100 pages is 100! = ~9.33262 * 10^157, so while the statement "there are more than 32m possible combinations" is correct, the earlier statement that it "has 32m possible combinations" is hugely off the mark!

It's conceivable that there are enough easy constraints (e.g. along 'page N cannot possibly follow page M because a sentence that's split between the two makes no sense whatsoever' lines) to reduce the 100! combinations to just 32m combinations that are at all plausible. But I cannot help thinking that it's even more plausible that somewhere along the line, someone simply dreamt up a number that the general populace would consider impressively big... (And if I had to guess where along the line, the original publication date of 1934 seems plausible - inflation and the development of computers since then has probably grown the proportion of the population that regards 32 million as not all that big a number a bit too much, so I would expect a modern-day dreamt-up number to involve billions or even trillions instead of mere millions...)

Gengulphus

This article:

https://www.lrb.co.uk/blog/2020/novembe ... ailor.-ugh

says the number 32 million was a ‘purely arbitrary number’ according to Patrick Wildgust who revived the book. The article's author cites the actual number Gengulphus calculated as almost "a hundred unquinquagintillion". You learn something new every day...


GS

I wrote:It's conceivable that there are enough easy constraints (e.g. along 'page N cannot possibly follow page M because a sentence that's split between the two makes no sense whatsoever' lines) to reduce the 100! combinations to just 32m combinations that are at all plausible. ...

I can add that that particular type of easy constraint looks to have been designed out of the puzzle, judging by the photographs in one of the reviews in https://www.amazon.co.uk/Cains-Jawbone- ... 1783527412: all the starts and ends of pages that are visible in them are at starts and ends of sentences.

Gengulphus

British comedy writer John Finnemore has solved Cain’s Jawbone, a murder mystery that has 32m possible combinations

Does that wording have to refer to page ordering? "murder mystery ... possible combinations" could be something more like a game of cluedo. It was Colonel Sanders, in the takeaway, with the poison!

In that context, 32 million would indeed seem a lot.

UncleEbenezer wrote:

British comedy writer John Finnemore has solved Cain’s Jawbone, a murder mystery that has 32m possible combinations

Does that wording have to refer to page ordering? "murder mystery ... possible combinations" could be something more like a game of cluedo. It was Colonel Sanders, in the takeaway, with the poison!

In that context, 32 million would indeed seem a lot.

According to the link https://www.lrb.co.uk/blog/2020/novembe ... ailor.-ugh posted by GoSeigen:

... There are two parts to the solution. First you have to provide the full names of the six murderers and their victims, and the order in which they died. That I managed. But – mindbendingly difficult though it was – that was the easy bit. The second part involves putting every one of the 100 pages in exactly the right sequence. According to the Laurence Sterne Trust there are ‘over 32 million’ permutations, but as Wildgust says, that’s a ‘purely arbitrary number’: the actual figure is many orders of magnitude over 32 million – closer to a hundred unquinquagintillion. Hats off to Finnemore.

It's conceivable that there are 32 million combinations for the first part of the solution. E.g. if there are 12 first names and 12 surnames in the book, to be ordered e.g. as first name of first murderer, surname of first murder, first name of first victim, surname of first victim, followed by similar lists for the second murder, the third murder, etc, that would be exactly what is needed for the first part of the solution. That would mean that there are (12!)^2 = 229,442,532,802,560,000 possibilities for the first part of the solution - considerably more than 32 million, but it could be reduced quite a lot if e.g. people shared surnames and/or first names, or some of the murderers were later victims, etc. But it takes quite a lot to bring it down to somewhere in the region of 32 million. E.g. if there are just 7 people with 7 different first names and 7 different last names, and the solution involves person 6 murdering person 7, then person 5 murders person 6, etc, until finally person 1 murders person 2, a similar argument says that there are (7!)^2 = 25,401,600 possibilities for the first part of the solution, i.e. a number of roughly the same order of magnitude as 32 million. That's a bit too restrictive to achieve "more than 32 million", but relaxing the restrictions even slightly from that is likely to multiply the number of possibilities by a large factor and so make the number of possibilities much more than 32 million.

And since it suggests that the number of possibilities for the first part of the solution is much bigger than 32 million, and the number of possibilities for the second part of the solution is close to a hundred unquinquagintillion, the number of possibilities for the full solution is much greater than a hundred unquinquagintillion! So it seems highly likely to me that Wildgust (Patrick Wildgust of the Laurence Sterne Trust) is correct about 32 million being a ‘purely arbitrary number’.

Gengulphus

Does anyone know if there's a simpler version of such a puzzle available? Just as challenging but less time consuming perhaps. Sounds like an ideal Christmas present for someone I know!