BOMARBLE - D - Playing with Marbles

no tags 



Pablo was assigned in his class to construct pentagons inside pentagons with marbles but he doesn’t know how many marbles he will need. He knows that for one pentagon he needs 5 marbles


The only way he knows to insert a second pentagon is putting a marble in the middle of each segment and drawing three lines as shown. He puts a marble in the intersecting lines and removes them. To insert a third pentagon inside he first divides all segments in two including the ones that are not needed, and repeats the procedure. Drawing a second pentagon will require 12 marbles. A third pentagon will require 22 marbles. Given the information of how many pentagons will be created, write a program to calculate the number of marbles needed.


The input contains several test cases. Each test case contains one integer N indicating the number of pentagons to create (1<=N<=103). The end of input is indicated by a line containing only one zero.


For each test case in the input, your program must print a single line, containing one single integer, the number of marbles required. 

Sample Input

Sample Output

hide comments
ade_ramadhan: 2020-10-19 14:52:21

arithmatic multilevel formula after u got the pattern, each case become O(1)

ashutoshkumar6: 2018-10-23 20:03:51

ac in one go.....just observe the pattern of position of marble and try to find out a formula

shivamyadav00: 2018-10-21 14:04:08

thank you @DreamBig....for more test cases.

shashankpathak: 2018-09-14 23:01:39

Easy find Ap pattern!!

pratapvidhu_17: 2018-01-13 15:08:17

why this formula (a=(5*n+((n*n+n)/2)+(pow(2,n-1))-3) (n>1)is not accepted :/ ?? as it gives same value as formula for accepted one....

Last edit: 2018-01-13 15:08:51
sandilya1599: 2018-01-11 17:36:05


v_pp_27: 2017-11-08 19:24:42

100 th....!

epsilonalpha: 2017-06-12 12:03:44

AC in one go. Easy recurrence. :)

sagnik_66: 2017-06-06 09:27:47

Solved using both formula and dp :)

ajeetk_973: 2017-04-02 05:19:37

hell easy with recursion||dp|| just formula

Added by:Alvaro Javier Medina Balboa
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:C CPP C++ 4.3.2 JAVA