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 .
Answer Choices:
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Solution:
In the alphabet the letter is adjacent to both and . So in any rearrangement, can only be adjacent to , and thus must be the first or last letter in the rearrangement. Similarly, the letter can only be adjacent to , so must be the first or last letter in the rearrangement. Thus the only acceptable rearrangements are and .
The problems on this page are the property of the MAA's American Mathematics Competitions