It all assumes that the tunnel is perfectly straight and perpendiculat to the flat outer surface of a cover.
If the three volumes formed one homogenous cuboid, there could be, in a different definition, a tunnel from the bottom left front vertex to the right back top vertex.
Ah, yes. This can be a problem when drafting teasers. Too much information or too many limitations = “no teaser”
In this teaser, explaining how the bookworm reaches the start point could render the teaser pointless. Likewise, adding limitations such as ‘no diagonal moves’, ‘no going round in circles’ etc, might well require the publication of a 1 and 3/4 inch thick book to provide all the details …
I like your large diagonal move, but without the height and width of the books …
I got intrigued by this, and thought of a different way to look at it.
I first though, chance of one Welsh team drawing another is 2/15. But there is indeed only 3 possible combinations of an all Welsh tie up out of 120 possible combinations.
However, in the apporach there is a a possibility of a Welsh team drawing a non-Welsh team 13/15 but that another Welsh team draws a Welsh team of the 13 remaining teams, so 1/13 chance on that. Combined there are 2/13 + 13/15 x 1/13 which gives 3/15 or 20%.
In the second approach the 1/40 is correct but you ned to consider that there are 8 matches which means that you have 8 chances to make the 1/40, so 1/40 x 8 which gives 8/40 or 20%.
Welcome back to posting on the forum and well done !
Your solution produces the same result as Ravvie’s final solution. So this is a great relief and further reassurance that we now have a good solution to Ravvie’s teaser.
Based on Mike’s contribution, perhaps the teaser would be more obvious, and lead to my anticipated solution, if that first sentence simply stated “An industrious bookworm has bored its way from page one of Vol I to the last page of Vol III”
I now see why and how the hints that have been posted could suggest a variety of different answers.
Oh dear, must try better next time !!
Still, it would be nice if you could all post your solutions.
No. Think of it as being square with side 2mm, and its 25.4 mm long.
We are only interested in the worm’s journey from page 1 of Vol I to the last page of Vol III, and the books are all standard English hardbacks, not Arabic, Chinese or Japanese etc.
The worm takes the shortest route and we are only concerned with the distance travelled by the ‘nose’ of the worm - it’s length, 25.4 mm, is not important.
I’m appalled at how badly I worded this teaser. But with grateful thanks to all who have posted, I’m certain I shall improve the next time I use it
Based on the wording on the spine ‘Vol I’ etc, and the arrangement of the volumes L to R, I think we should assume conventional western format. Or, these might be modern Japanese technical, or scientific books, which I understand conform with the conventional western format.
But how does the worm start at page 1 of Vol 1? It is on the inner side of the row of books, so would need to tunnel first to page 1, and then if it travels from page one it then journeys back again to the end of the pages in volume 1 before heading back again to Vol 2. The use of “from” is ambiguous- it can mean either just including every page, or every page in numerical order.
It might have tunnelled its way up through the bookshelf, or been laid as an egg sometime earlier and started boring when it matured, or …
… next time I think I should try to clarify that however it got to page 1 of Vol I is not too important. We are only interested in how it then gets to the last page of Vol III (conventional meaning of last page in a book eg Page No 503 in a book with 503 pages) by the shortest possible route.
I think I need a bit more practise writing Civil Engineering Specifications, it might help with writing teasers …