Task — Four squares puzzle

You are given four squares as above with numbers named a, b, c, d, e, f, g.

Write a script to place the given numbers in the boxes so that sum of the numbers in each box is the same.

Examples

Example 1
Input: 1,2,3,4,5,6,7
Output:
    a = 6
    b = 4
    c = 1
    d = 5
    e = 2
    f = 3
    g = 7
    Box 1: a + b = 6 + 4 = 10
    Box 2: b + c + d = 4 + 1 + 5 = 10
    Box 3: d + e + f = 5 + 2 + 3 = 10
    Box 4: f + g = 3 + 7 = 10

Analysis

This is an an interesting challenge. I pondered some shortcuts to the answer, but concluded that simply checking all the permutations of the given 7 numbers would be fast enough, and indeed that finds a solution in less than a second - or if there is no solution, meaning it has to try every permutation, it's just as fast.

Interestingly, the solution I found for the supplied 7 digits - 3, 7, 2, 1, 5, 4, 6 - is different from the one in the example.

I also tried using 7 random numbers in the range 0 - 20 and found quite a few solutions - around 5% of the ones I tried.

Try it 

#!/usr/bin/perl

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

use v5.26;    # The Weekly Challenge - 2021-04-19
use utf8;     # Week 109 - task 2 - Four squares puzzle
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;
use Algorithm::Combinatorics 'permutations';

four_squares_puzzle(1, 2, 3, 4, 5, 6, 7);
four_squares_puzzle(3, 4, 5, 6, 7, 8, 9);
four_squares_puzzle(4, 5, 6, 7, 8, 9, 10);
four_squares_puzzle(5, 6, 7, 8, 9, 10, 11);
four_squares_puzzle(13, 9, 5, 5, 8, 6, 14);
four_squares_puzzle(1, 6, 16, 17, 5, 6, 17);

sub four_squares_puzzle {
    
    my (@d, $i, $sum, $p, $a, $b, $c, $d, $e, $f, $g);
    
    # initialise
    @d = @_;
    say qq[\nInput:  ] . join(', ', @d);
    $i = permutations(\@d);
    
    # loop over permutations
    while ($p = $i->next) {
        ($a, $b, $c, $d, $e, $f, $g) = @$p;
        $sum = $a + $b;
        
        # success?
        if ($b + $c + $d == $sum and
            $d + $e + $f == $sum and
            $f + $g == $sum) {
            say qq[Output: a = $a, b = $b, c = $c, d = $d, e = $e, f = $f, g = $g];
            printf("a + b     = %2d + %2d       = %2d\n", $a, $b, $a + $b);
            printf("b + c + d = %2d + %2d + %2d  = %2d\n", $b, $c, $d, $b + $c +$d);
            printf("d + e + f = %2d + %2d + %2d  = %2d\n", $d, $e, $f, $d + $e + $f);
            printf("f + g     = %2d + %2d       = %2d\n", $f, $g, $f + $g);
            return;
        }
    }
    
    # failure
    say qq[Output: no solution found];
}

18 lines of code

I completed this challenge after the closing date
and it has not been submitted to GitHub

Output

Input:  1, 2, 3, 4, 5, 6, 7
Output: a = 3, b = 7, c = 2, d = 1, e = 5, 
   f = 4, g = 6
a + b     =  3 +  7       = 10
b + c + d =  7 +  2 +  1  = 10
d + e + f =  1 +  5 +  4  = 10
f + g     =  4 +  6       = 10

Input:  3, 4, 5, 6, 7, 8, 9
Output: a = 7, b = 8, c = 3, d = 4, e = 5, 
   f = 6, g = 9
a + b     =  7 +  8       = 15
b + c + d =  8 +  3 +  4  = 15
d + e + f =  4 +  5 +  6  = 15
f + g     =  6 +  9       = 15

Input:  4, 5, 6, 7, 8, 9, 10
Output: a = 9, b = 8, c = 5, d = 4, e = 6, 
   f = 7, g = 10
a + b     =  9 +  8       = 17
b + c + d =  8 +  5 +  4  = 17
d + e + f =  4 +  6 +  7  = 17
f + g     =  7 + 10       = 17

Input:  5, 6, 7, 8, 9, 10, 11
Output: no solution found

Input:  13, 9, 5, 5, 8, 6, 14
Output: a = 13, b = 6, c = 8, d = 5, e = 9, 
   f = 5, g = 14
a + b     = 13 +  6       = 19
b + c + d =  6 +  8 +  5  = 19
d + e + f =  5 +  9 +  5  = 19
f + g     =  5 + 14       = 19

Input:  1, 6, 16, 17, 5, 6, 17
Output: a = 6, b = 17, c = 5, d = 1, 
   e = 16, f = 6, g = 17
a + b     =  6 + 17       = 23
b + c + d = 17 +  5 +  1  = 23
d + e + f =  1 + 16 +  6  = 23
f + g     =  6 + 17       = 23