# Where's that book you want?

A friend of yours, studying law, just walked out of the library and you have a short social talk. During the conversation it comes to pass which books he just returned. One of the books seemed interesting to you and you ask your friend where'd he put it, because sadly the old cranky library doesn't have an organized and indexed system for their shelves. Your friends tell you it's in the 5th lane on the left hand side coming from the back. He says it's in the somewhere between the 7th from the left and the 49th of the right on the 3rd row. When you enter the library you notice the shelves have predefined trays for a book, meaning the book size doesn't matter and each tray always consumes the same space. You see a small specification sticker on the shelve saying a whole row contains 83 trays.

The library consists of 11 back-to-back lanes, with the first lane at the entrance also having shelves on the back-side, facing towards the entrance. All shelves are 6 rows high.

Giving that all the books slightly average the same size as the book you mentioned to your friend:

1.) In which tray(s) can you find the book when you come in from the front?

2.) How many space for books is there in the whole library?

• I don't see what the puzzle is. Your friend tells you the position of the book, and the puzzle is to work out what the position of the book is? I'm also very confused about the configuration of the library shelves - I can't picture what you mean by "lane", "back to back", "trays", etc. – Jack M May 10 '15 at 22:59

1)

5th lane from the back is 7th lane from the front.
swap left and right, so the book is between the 49th from the left and 7th from the right on the 3rd row.

2)

since the first lane is double there should be $12 * 6 * 83 = 5976$ spaces