Python: Find the number of combinations of a,b,c and d

Last update on May 24 2025 10:47:27 (UTC/GMT +8 hours)

Sum Combinations Counter

Write a Python program that reads an integer n and finds the number of combinations of a,b,c and d (0 = a,b,c,d = 9) where (a + b + c + d) will be equal to n.

Input:
n (1 ≤ n ≤ 50)
Input the number(n): 15
Number of combinations: 592

Sample Solution:

Python Code:

# Import the itertools module to work with iterators and combinatorial functions
import itertools

# Prompt the user to input a number 'n'
print("Input the number(n):")

# Read the user input and convert it to an integer
n = int(input())

# Initialize the variable 'result' to store the count of combinations
result = 0

# Iterate over all combinations of (i, j, k) where i, j, k are in the range [0, 9]
for (i, j, k) in itertools.product(range(10), range(10), range(10)):
    # Check if the sum of i, j, and k lies between 0 and 9 (inclusive)
    result += (0 <= n - (i + j + k) <= 9)

# Print the number of combinations that satisfy the condition
print("Number of combinations:", result)

Sample Output:

Input the number(n):
 15
Number of combinations: 592

Explanation:

The above Python code prompts the user to input a number 'n' and then counts the number of combinations of three digits (i, j, k), where each digit ranges from 0 to 9, such that their sum is equal to 'n'. The code utilizes the itertools module to generate all possible combinations of (i, j, k) and increments a counter 'result' whenever the sum of these digits falls between 0 and 9 (inclusive).

Finally, it prints the count of combinations that satisfy the given condition.

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to count the number of combinations of four digits whose product equals a given number.
• Write a Python program to count the number of unique combinations of four digits that sum to a given target where no digit repeats.
• Write a Python program to count the number of ways a subset of numbers from a list can sum up to a target value.
• Write a Python program to compute the number of combinations of four non-negative integers that sum to a given number using dynamic programming.

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Python Code Editor:

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