Problem 55360. Magical Land

• Created by Dyuman Joshi

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Mother Earth has gifted humanity a magical land to help all life on earth, in the shape of a n-sided regular polygon.

You, being a good samaritan has volunteered to help.

The land has directional properties, and is to be divided accordingly. The magical properties can only be utilized if the following conditions are met -

1. All divided parts must be quadrilaterals.
2. Exactly (n/2-1) people should have the access to the land. One part (quadrilateral) per person.

For example

n=6 %A regular hexagon to be divided in 6/2-1 = 2 parts

There are 3 ways of dividing -

1 > ABCDA-DEFAD

2 > BCDEB-EFABE

3 > CDEFC-FABCF

%ABCDA, BCDEB and CDEFC are identical on paper, but since the land has directional properties

%they are counted different here

n=8 %A regular octagon to be divided in 8/2-1 = 3 parts

1 > ABCDA-DEFGD-ADGHA

2 > ABCDA-DEHAD-EFGHE

%and so on

So, Given n, return, in how many ways the land can be divided according to the conditions.

note - n will be an even natural number.

Solve

Solution Stats

70.0% Correct | 30.0% Incorrect

• 10 Solutions
• 7 Solvers

Last Solution submitted on Jul 05, 2024

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