perplexus.info :: Numbers : Permutations count

Permutations count (Posted on 2015-10-01)

Find the number of permutations of (1,2,3...n) possessing the following feature:

The number n is the only local maximum e.g. 123465, 123564, 654321,
as opposed to 651432, 261354.

Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

Solution: (Hide)

Let f(n)=k.
To evaluate f(n) note that for each one of k permutations you can get two new ones by inserting the number n+1 before or after n.
So f(n+1)=2*k.
f(1)=1 implies f(n) =2^(n-1)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: error in	Ady TZIDON	2015-10-02 21:29:54
error in "official solution"	Steve Herman	2015-10-02 19:02:32
My misleading subject line.	Jer	2015-10-02 13:38:33
one general remark	Ady TZIDON	2015-10-02 13:16:01
re(2): I guess simplicity is in the mind of the user	Ady TZIDON	2015-10-02 12:57:26
re: I guess simplicity is in the mind of the user	Steve Herman	2015-10-02 12:10:50
I guess simplicity is in the mind of the user	Charlie	2015-10-02 09:57:08
Simpler solution	Jer	2015-10-02 07:28:14
re: solution	Ady TZIDON	2015-10-02 00:00:20
solution	Charlie	2015-10-01 16:02:09

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