Books and Spines

[stormin]

Imagine that someone has stacked a large number of books in a row so that the spines and non spines alternate. On one side of the line you count 99 spines. On the other side you again count 99 spines. What is the maximum number of books there can be in the row? 198 seems to be too obvious.

[Salty]

The only thing I can think of is that the two sides you count are not the one with the alternating spine/non-spine.

The stack has 4 sides, and assume the question means the side facing you has alternating spine/non-spine. To achieve this, the non-spine books could have their spine facing away from you, to the right or to the left. Assume that you place 99 of the "non-spine" books with their spine to the left and a further 99 "non-spine" books with their spine to the right. All the rest of the books have their spine towards you ("spine") or directly away from you ("non-spine"). When you count the two sides, you count the left and right sides, getting 99 in each case. The front side ("spines") has a minimum of 197 spines (as there are at least 198 "non-spines" facing you to put "spines" between). You could then stack alternative spines facing you and spines directly away from you for as long as you want without altering the 99 spines on left and right.

Conclusion: You could have an infinite number of books!

This can't be the right answer, can it?

[Dinkypuzzled]

I tried a different tack and came up with 396 as the answer.

Try a simpler case.Take four books - two spines facing and two non-spines facing. It is possible to interlock the four books (each half-open). You can now fit in 2 non spines on each side. This effectively hides the non spine books so you can fit in more. My theory means you can fit in 99 each side making a total of 198 + 198 = 396.

[loobylou]

I think the answer is 199. Assume you see the same spines from both sides of the table -ie the books' spines either face the ceiling or face the top of the table. So you have 99 spines of books facing the ceiling and 99 spines of books facing the table - total 198. So to fulfil the question you need another book at the end of the row facing the top of the table - 199.