Six different books $(A,B,C,D,E,F)$ of identical size are stacked as in the figure.
We know
$A$ and $D$ are not touching.
$E$ is between two books which are both vertical or both horizontal.
$C$ touches exactly two books.
$A$ and $F$ touch.
Question:
If in addition we know
$E$ and $F$ touch along their cover (long side), how many books will have their positions known?
Moreover, is there a general approach to such questions? I did not see how to use adjacency matrix to much benefit.
Puzzles like this are usually intended to be solved by hand.
The first clue about $E$ says it is book $2$ or $5$. $C$ can be $2,4$ or $6$. The only book we can be sure of is $D$ in position $1$. It can't be $E$ or $C$. If it is $A$, we must have $F$ in $2$, which contradicts the information on $E$. If it is $F$, it can't touch both $E$ and $A$. If it is $B$, and $EF$ are next to it, either $AD$ touch or $C$ has no home. If it is $B$ and $EF$ are horizontal, then $A$ has to touch $D$. To show that is all, we can display two choices for the others: $123456$ can be $DEFCAB$ or $DBAFEC$.