Python Program to Find all Numbers in a Range which are Perfect Squares and Sum of all Digits in the Number is Less than 10

When it is required to find all numbers in a range that are perfect squares and the sum of digits in the number is less than 10, list comprehension is used. A perfect square is a number that can be expressed as the product of an integer with itself.

Below is the demonstration of the same −

Example

lower_limit = 5
upper_limit = 50
numbers = []
numbers = [x for x in range(lower_limit, upper_limit + 1) if (int(x**0.5))**2 == x and sum(list(map(int, str(x)))) < 10]
print("The result is:")
print(numbers)

Output

The result is:
[9, 16, 25, 36, 49]

How It Works

Let's break down the algorithm step by step ?

# Check if a number is perfect square
def is_perfect_square(n):
    sqrt_n = int(n**0.5)
    return sqrt_n * sqrt_n == n

# Calculate sum of digits
def sum_of_digits(n):
    return sum(int(digit) for digit in str(n))

# Find numbers in range
lower = 1
upper = 100
result = []

for num in range(lower, upper + 1):
    if is_perfect_square(num) and sum_of_digits(num) < 10:
        result.append(num)
        
print("Perfect squares with digit sum < 10:")
print(result)

Perfect squares with digit sum < 10:
[1, 4, 9, 16, 25, 36, 49, 64, 81]

Using List Comprehension

The same logic can be implemented more concisely using list comprehension ?

lower = 1
upper = 100

# One-liner using list comprehension
result = [x for x in range(lower, upper + 1) 
          if (int(x**0.5))**2 == x and sum(int(d) for d in str(x)) < 10]

print("Perfect squares with digit sum < 10:")
print(result)

# Let's also show the digit sums for verification
for num in result:
    digit_sum = sum(int(d) for d in str(num))
    print(f"{num}: digit sum = {digit_sum}")

Perfect squares with digit sum < 10:
[1, 4, 9, 16, 25, 36, 49, 64, 81]
1: digit sum = 1
4: digit sum = 4
9: digit sum = 9
16: digit sum = 7
25: digit sum = 7
36: digit sum = 9
49: digit sum = 13
64: digit sum = 10
81: digit sum = 9

Key Points

• Perfect square check: (int(x**0.5))**2 == x verifies if a number is a perfect square

• Digit sum calculation: sum(int(d) for d in str(x)) converts number to string, then sums individual digits

• List comprehension provides a concise way to filter numbers based on multiple conditions

• The condition < 10 ensures only numbers with single-digit sum are included

Conclusion

This program efficiently finds perfect squares within a range where the sum of digits is less than 10 using list comprehension. The key is combining perfect square detection with digit sum calculation in a single filtering condition.