2015 AMC 10A Problems/Problem 10
Revision as of 18:05, 4 February 2015 by BeastX-Men (talk | contribs) (→Solution: Added LaTeX in a few places.)
Problem
How many rearrangements of 
are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either 
or 
.
$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}}\ 3\qquad\textbf{(E)}\ 4$ (Error compiling LaTeX. Unknown error_msg)
Solution
Observe that we can't begin a rearrangement with either 
or 
, leaving 
and 
, respectively.
Starting with 
, there is only one rearrangement: 
. Similarly, there is only one rearrangement when we start with 
: 
.
Therefore, our answer must be 
.
