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Count the acceptable permutations (Posted on 2023-10-30) Difficulty: 3 of 5
How many permutations of the integers 1, 2, …, n are there such that every integer (last excluded) is followed by (not necessarily immediately) by an integer which differs from it by 1?

For example if n=4 the permutation 1432 is an acceptable one, while 2431 is not.

  Submitted by Ady TZIDON    
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Solution: (Hide)
N=2^( n-1). Easy to prove by induction. See Larry’s proof fortified by S.Herman’‘s‘ extension

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle ThoughtsK Sengupta2024-04-02 22:01:16
re: Most of a proofSteve Herman2023-10-30 20:39:05
Some ThoughtsMost of a proofLarry2023-10-30 14:03:53
Some Thoughtscomputer exploration -- no proof -- spoilerCharlie2023-10-30 12:08:50
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