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2007 AMC 12A Question 25

AMC12 · 2007 AMC 12A

Question 25

Call a set of integers *spacy* if it contains no more than one out of any three consecutive integers. How many subsets of $\{1,2,3,\ldots,12\},$ including the empty set, are spacy?
  1. $121$
  2. $123$
  3. $125$
  4. $127$
  5. $129$