Python: Find four positive even integers whose sum is n

Last update on April 17 2025 13:08:56 (UTC/GMT +8 hours)

Four Even Integers Summing to n

Write a Python program to find four positive even integers whose sum is a given integer.

Input:
n = 100
Output:
[94, 2, 2, 2]

Input:
n = 1000
Output:
[994, 2, 2, 2]

Input:
n = 10000
Output:
[9994, 2, 2, 2]

Input:
n = 1234567890
Output:
[1234567884, 2, 2, 2]

Sample Solution:

Python Code:

# License: https://bit.ly/3oLErEI

# Function to find four positive even integers whose sum is equal to a given number
def test(n):
    # Iterate over possible values for the first even integer (a)
    for a in range(n, 0, -1):
        # Skip odd values for a
        if not a % 2 == 0:
            continue
        
        # Iterate over possible values for the second even integer (b)
        for b in range(n - a, 0, -1):
            # Skip odd values for b
            if not b % 2 == 0:
                continue
            
            # Iterate over possible values for the third even integer (c)
            for c in range(n - b - a, 0, -1):
                # Skip odd values for c
                if not c % 2 == 0:
                    continue
                
                # Iterate over possible values for the fourth even integer (d)
                for d in range(n - b - c - a, 0, -1):
                    # Skip odd values for d
                    if not d % 2 == 0:
                        continue
                    
                    # Check if the sum of a, b, c, and d equals the target number
                    if a + b + c + d == n:
                        # Return the list of found even integers
                        return [a, b, c, d]

# Test cases with different values of n
n = 100
print("Four positive even integers whose sum is", n)
print(test(n))

n = 1000
print("\nFour positive even integers whose sum is", n)
print(test(n))

n = 10000
print("\nFour positive even integers whose sum is", n)
print(test(n))

n = 1234567890
print("\nFour positive even integers whose sum is", n)
print(test(n))

Sample Output:

Four positive even integers whose sum is 100
[94, 2, 2, 2]

Four positive even integers whose sum is 1000
[994, 2, 2, 2]

Four positive even integers whose sum is 10000
[9994, 2, 2, 2]

Four positive even integers whose sum is 1234567890
[1234567884, 2, 2, 2]

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to determine four positive even integers that add up to a given integer n, using algebraic manipulation.
Write a Python program to solve for four even numbers whose sum is n by setting three to the minimum even value and computing the fourth.
Write a Python program to output a list of four even integers that sum to n, ensuring the first element is maximized.
Write a Python program to implement a function that returns a quadruple of even numbers whose sum equals n, with three fixed as 2.

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