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- Magic Number of coding-:A number is said to be a magic number,if summing the digits of the number and then recursively repeating this process for the given sumuntill the number becomes a single digit number equal to 1. Example: Number = 50113 => 5+0+1+1+3=10 => 1+0=1 [This is a Magic Number] Number = 1234 => 1+2+3+4=10 => 1+0=1 [This is a Magic Number] Number = 199 => 1+9+9=19 => 1+9=10 => 1+0=1 [This is a Magic Number] Number = 111 => 1+1+1=3 [This is NOT a Magic Number].Magic Number Code question::-1.A number is said to be a magic number,if summing the digits of the number and then recursively repeating this process for the given sumuntill the number becomes a single digit number equal to 1. Example: Number = 50113 => 5+0+1+1+3=10 => 1+0=1 [This is a Magic Number] Number = 1234 => 1+2+3+4=10 => 1+0=1 [This is a Magic Number] Number = 199 => 1+9+9=19 => 1+9=10 => 1+0=1 [This is a Magic Number] Number = 111 => 1+1+1=3 [This is NOT a Magic Number].1. Recursive Multiplication Write a recursive function that accepts two arguments into the parameters x and y. The function should return the value of x times y. Remember, multiplication can be performed as repeated addition as follows: 7* 4 = 4 + 4 + 4 +4 + 4 + 4 + 4
- Recursive Power MethodWrite a method called powCal that uses recursion to raise a number to a power. The method should accept two arguments: The first argument is the exponent and the second argument is the number to be raised (example” powCal(10,2) means 210). Assume that the exponent is a nonnegative integer. Demonstrate the method in a program called Recursive (This means that you need to write a program that has at least two methods: main and powCal. The powCal method is where you implement the requirements above and the main method is where you make a method call to demonstrate how your powCal method work).python def factorial(n):pass # replace this line with your lines of recursive codedef sum_recursively(n):pass # replace this line with your lines of recursive codedef sumlist_recursively(l):pass # replace this line with your lines of recursive codedef reverse_recursively(l):pass # replace this line with your lines of recursive code#EXTRA CREDITdef multiply_recursively(n, m):pass # replace this line with your lines of recursive codepython def factorial(n):pass # replace this line with your lines of recursive codedef sum_recursively(n):pass # replace this line with your lines of recursive codedef sumlist_recursively(l):pass # replace this line with your lines of recursive codedef reverse_recursively(l):pass # replace this line with your lines of recursive code#EXTRA CREDITdef multiply_recursively(n, m):pass # replace this line with your lines of recursive code
- python def factorial(n):pass # replace this line with your lines of recursive codedef sum_recursively(n):pass # replace this line with your lines of recursive codedef sumlist_recursively(l):pass # replace this line with your lines of recursive codedef reverse_recursively(l):pass # replace this line with your lines of recursive code#EXTRA CREDITdef multiply_recursively(n, m):pass # replace this line with your lines of recursive codeRecursive Power FunctionWrite a function that uses recursion to raise a number to a power. The function should accept two arguments: the number to be raised and the exponent. Assume that the exponent is a nonnegative integer. Demonstrate the function in a program. SAMPLE RUN #0: ./recursiveExponent Hide Invisibles Highlight: Show Highlighted Only 2^3=8↵ 2^4=16↵ 3^3=27↵ 6^3=216↵ 7^7=823543↵ 10^9=1000000000↵Lab Goal : This lab was designed to teach you more about recursion. Lab Description : luckyThrees will return a count of the 3s in the number unless the 3 is at the start. A 3 at the start of the number does not count. /* luckyThrees will return the count of 3s in the number* unless the 3 is at the front and then it does not count* 3 would return 0* 31332 would return 2* 134523 would return 2* 3113 would return 1* 13331 would return 3* 777337777 would return 2* the solution to this problem must use recursion*/public static int luckyThrees( long number ){} Sample Data : 331332134523311313331777337777 Sample Output : 022132
- 7. Recursive Power Method In Python, design a function that uses recursion to raise a number to a power. The function should accept two arguments: the number to be raised, and the exponent. Assume the exponent is a nonnegative integer.3-The following pattern of numbers is called Pascal's triangle. 1 1 1 14 641 The numbers at the edge of the triangle are all 1, and each number inside the triangle is the sum of the two numbers above it. Write a procedure that computes elements of Pascal's triangle by means of a recursive process. 1 1 1 2 1 3 3Use the template below: def createList(n): #Base Case/s #ToDo: Add conditions here for base case/s #if <condition> : #return <value> #Recursive Case/s #ToDo: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once all ToDo is completed return [] def removeMultiples(x, arr): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all ToDo return [] def Sieve_of_Eratosthenes(list): #Base Case/s if len(list) < 1 : return list #Recursive Case/s else: return [list[0]] + Sieve_of_Eratosthenes(removeMultiples(list[0], list[1:])) if __name__ == "__main__": n = int(input("Enter n: "))…