index.php

<?php
//require 'dataset.php';
$data = [42, 88, 100, 103, 112, 115, 124, 161, 170, 185];

$possibilities = createPossibilities($data);
 
$result = getResult($possibilities, $data);
var_dump($result);
//output array(5) {
//  [0]=>
//  int(15)
//  [1]=>
//  int(27)
//  [2]=>
//  int(73)
//  [3]=>
//  int(88)
//  [4]=>
//  int(97)
//}

function createPossibilities(array $data): array
{
    $possibilities = [];
    for ($k=0; $k<count($data); $k++) {
        for ($i=1; $i<=100; $i++) {
            for ($j=1; $j<=100; $j++) {
                if ($i !== $j && $i + $j === $data[$k]) {
                    $possibilities[$data[$k]][] = [$i, $j];
                }
            }
        }
    }
    return $possibilities;
}

function getResult(array $possibilities, array $data): ?array
{
    foreach ($possibilities[$data[0]] as $key => $paires) {
        foreach ($possibilities as $secondPaires) {
            foreach ($secondPaires as $pairesToMerge) {
                for ($i=1; $i<=100; $i++) {
                    $probables = array_merge($paires, $pairesToMerge, [$i]);
                    if (isCorrect($data, $probables)) {
                        return $probables;
                    }
                }

            }
        }
    }
    return null;
}


function isCorrect(array $inputs, array $probables): bool
{
    $find = 0;
    foreach ($inputs as $number) {
        if (isThereAPair($probables, $number)) {
            $find += 1;
        }
    }
    return $find === count($inputs);
}


function isThereAPair(array $probables, int $number): bool
{
    for ($i=0; $i<count($probables); $i++) {
        for ($j=0; $j<count($probables); $j++) {
            if ($probables[$i] + $probables[$j] === $number) {
                return true;
            }
        }
    }
    return false;
}