# Book stacking brain teaser

I've been given a puzzle, and I just can't work out an answer. Can you help?

I'd also like to know your thought process for solving, as this matters more than the correct answer. Does it belong to a pattern of puzzles?

The scenario is this:

• There are six books by six different authors - J,K,L,M,N and O - which are to be placed on a bookcase with six shelves.
• The shelves are numbered from one, the highest, to six, the lowest, and exactly one book will be placed on each shelf.
• The book K must be on the second shelf below the book J
• The book O must be placed on either the first or sixth shelf.
• The book L cannot be placed on either the shelf immediately above or the shelf immediately below the book by M.

Which one of the following is TRUE?

1. K and L CANNOT be placed on shelves three and four respectively
2. M and N CANNOT be placed on shelves three and four respectively
3. J and M CANNOT be placed on shelves three and four respectively
4. L and K CANNOT be placed on shelves three and four respectively
5. N and J CANNOT be placed on shelves three and four respectively

Thanks!

I think that the answer is:

$2$ and is only constrained by the first rule (about J and K).
J and K have exactly 1 shelf between them. That means that they span 3 shelves. So, no matter the arrangement, either J or K must be one of the shelves 3 or 4.
So, any solution that fills both 3 and 4 with neither J nor K can't happen.

• Bah, got yours in as I was typing mine! Glad we came to the same conclusion, though! – Josh Feb 27 '15 at 21:49
• aha thanks Jon and Josh.. I was being blind.. so easy now I look at it again! – Stretch Feb 27 '15 at 21:51
• Well, there are 2 red herring clues, and lots of negatives, so that makes figuring out an answer a bit tougher. – JonTheMon Feb 27 '15 at 21:52

The true statement is:

2. M and N CANNOT be placed on shelves three and four respectively.

Why?

Book J can only occupy shelves 1, 2, 3, 4. Book K can only occupy shelves 3, 4, 5, 6. No matter where you place J and K, shelves 3 and 4 will always be occupied by one or the other. Proof: J on shelf 1, K on shelf 3. J on shelf 2, K on shelf 4. K on shelf 5, J on shelf 3. K on shelf 6, J on shelf 4.

• thanks Josh! JonTheMoon just beat you to it though! – Stretch Feb 27 '15 at 21:50