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’.