Mathematics Problem Solving Using Python (3 - 5)
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Numbers Question Number 10: 3:34
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Question 1:-
You are given a task to tell whether the number is pure or not. A pure number is a number whose sum of digits is multiple of 3.
O(1) time and O(1) space
Input Description:
You are given a number n.
Output Description:
Print yes if it is pure else not
Sample Input :
13
Sample Output :
not
************
a = input()
r = 0
for i in a:
r += int(i)
if r % 3 == 0:
print('yes')
else:
print('not')
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Question 2:-
You are given a set of numbers, out of which you have to tell which of them are finest. A finest number ‘n’ is a number which is formed by a number ‘t’ such that
n=t^3+(t+1)^3
t is a natural number
Input Description:
You are given a number ‘z’ representing total numbers in an array, Next line contains z space separated numbers.
Output Description:
Print the numbers which are finest in ascending order if there are no such numbers print -1.
Sample Input :
2
1729 189
Sample Output :
189 1729
***********
a = int(input())
arr = list(map(int, input().split()))
lst = []
form = 1
for i in arr:
for j in range(1,100+1):
form = j**3 + (j+1)**3
if i == form:
lst.append(i)
lst.sort()
print(*lst)
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Question 3:-
You are given a number ‘n’. You have to tell whether a number is great or not. A great number is a number whose sum of digits let (m) and product of digits let(j) when summed together gives the number back
m+j=n
Input Description:
You are given a number n;
Output Description:
Print Great if a number is great else print the no
Sample Input :
59
Sample Output :
Great
**********
n = int(input())
t = n
d = 1
r = 0
p = 1
while(n 'is greater than' 0):
d = n%10
r += d
n = n//10
p = d*p
A = r+p
if A == t:
print('Great')
else:
print('no')
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Question 4:-
You are given an array of non-negative integers representing height of walls at index i as Ai and the width of each block is 1. Compute how much air can be encapsulated between the walls of chamber.
Input Description:
Each line contains an integer ‘N’ denoting the size of the array Next line contains N space separated numbers to be stored in array.
Output Description:
Output the total unit of Air encapsulated between the walls of chamber.
Sample Input :
3
7 4 9
Sample Output :
3
***********
nos = int(input())
numlist = list(map(int, input().split()))
lower = numlist[0]
if numlist[nos-1] 'is lesser than' lower:
lower = numlist[nos-1]
air_in = 0
for ele in numlist[1:nos-1]:
if ele 'is lesser than' lower:
air_in += lower - ele
print(air_in)
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