Task — Sum of squares

You are given a number $N >= 10. Write a script to find out if the given number is such that sum of the squares of all its digits is a perfect square. Print 1 if it is otherwise 0.

Examples

Example 1
Input: $N = 34
Output: 1 as 3^2 + 4^2 => 9 + 16 => 25 => 5^2
Input: $N = 50
Output: 1 as 5^2 + 0^2 => 25 + 0 => 25 => 5^2
Input: $N = 52
Output: 0 as 5^2 + 2^2 => 25 + 4 => 29

Analysis

This is more-or-less explained in the task description:

• Split the number into its digits
• Sum the squares of the digits
• Test the sum for being a square

Such numbers are not sparse, though ones containing no repeats and no zeroes - like 12379 - are few and far between.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2021-06-07
use utf8;     # Week 116 - task 2 - Sum of squares
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

sum_of_squares(34);
sum_of_squares(52);
sum_of_squares(926);
sum_of_squares(9539);
sum_of_squares(12379);

sub sum_of_squares {
    
    my ($n, $squared, $is_good, $explain);
    
    # initialise
    $n = $_[0];
    
    # calculate sum of squares
    for (split('', $n)) {
        $squared += $_ ** 2;
        $explain .= qq[$_² + ];
    }
    
    # test for squareness
    $is_good = sqrt($squared) == int(sqrt($squared));
    
    # report
    $explain =~ s|\+ $|= |;
    say qq[\nInput:  $n];
    say qq[Output: ] . ($is_good ? qq[1 ∵ $explain] . sqrt($squared) . q[²] : '0');
}

last updated 2026-03-24 — 10 lines of code

Output

Input:  34
Output: 1 ∵ 3² + 4² = 5²

Input:  52
Output: 0

Input:  926
Output: 1 ∵ 9² + 2² + 6² = 11²

Input:  9539
Output: 1 ∵ 9² + 5² + 3² + 9² = 14²

Input:  12379
Output: 1 ∵ 1² + 2² + 3² + 7² + 9² = 12²