beautiful arrangements


  • 0
    J

    Lucy has N numbers from 1 to N. Her arrangement of those numbers is called a beautiful arrangement if any of the following is true:

    The number present at the ith position is divisible by i.
    i is divisible by the number present at the ith position.

    For a given N, how many beautiful arrangements are possible?

    Constraints

    1 < N < 20

    Function

    You are given a function arrangement that takes N as its argument and will return the total number of all possible beautiful arrangements.

    Sample Input

    2
    Sample Output

    2
    Explanation

    The number of possible beautiful arrangements for N=2 will be:
    1 2
    2 1

    Consider the arrangement [1, 2] then:

    number present at 1st position (i = 1) is 1, and 1 is divisible by i.
    number present at 2nd position (i = 2) is 2, and 2 is divisible by i.

    Consider the arrangement [2, 1] then:

    number present at 1st position (i = 1) is 2, and 2 is divisible by i.
    number present at 2nd position (i = 2) is 1, and i is divisible by 1.


  • 0

    @jagmag Welcome! If applicable, could you please add the company in the tags section?

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    This post is deleted!

  • 0
    B

    @jagmag said in beautiful arrangements:

    Lucy has N numbers from 1 to N. Her arrangement of those numbers is called a beautiful arrangement if any of the following is true:

    The number present at the ith position is divisible by i.
    i is divisible by the number present at the ith position.

    For a given N, how many beautiful arrangements are possible?

    Constraints

    1 < N < 20

    Function

    You are given a function arrangement that takes N as its argument and will return the total number of all possible beautiful arrangements.

    Sample Input

    2
    Sample Output

    2
    Explanation

    The number of possible beautiful arrangements for N=2 will be:
    1 2
    2 1

    Consider the arrangement [1, 2] then:

    number present at 1st position (i = 1) is 1, and 1 is divisible by i.
    number present at 2nd position (i = 2) is 2, and 2 is divisible by i.

    Consider the arrangement [2, 1] then:

    number present at 1st position (i = 1) is 2, and 2 is divisible by i.
    number present at 2nd position (i = 2) is 1, and i is divisible by 1.


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