Generates solutions for the maths puzzle for Vietnamese eight-year-olds. UPDATE: Missing quite a few answer combinations, see comment thread here: http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/may/20/can-you-do-the-maths-puzzle-for-vietnamese-eight-year-olds-that-has-stumped-parents-and-teachers#comment-52484375

output

8, 9, 6, 1, 3, 4, 7, 5, 2
8, 9, 3, 6, 5, 1, 2, 7, 4
7, 9, 3, 1, 2, 5, 6, 8, 4
9, 8, 2, 4, 5, 7, 6, 1, 3
7, 6, 1, 9, 5, 4, 2, 8, 3
9, 8, 6, 4, 5, 1, 7, 2, 3
7, 6, 1, 4, 3, 8, 9, 5, 2
5, 7, 1, 3, 4, 9, 8, 2, 6
7, 6, 4, 1, 3, 8, 5, 9, 2
8, 9, 6, 3, 5, 1, 2, 7, 4
7, 8, 4, 2, 5, 6, 9, 1, 3
9, 3, 6, 1, 5, 2, 7, 4, 8
7, 9, 1, 3, 2, 5, 6, 8, 4
7, 6, 4, 1, 3, 8, 9, 5, 2
7, 8, 2, 4, 3, 9, 6, 5, 1
7, 6, 1, 4, 3, 8, 5, 9, 2
7, 2, 1, 3, 5, 4, 8, 6, 9
5, 7, 3, 1, 4, 9, 8, 2, 6
9, 3, 6, 1, 5, 2, 4, 7, 8
1, 9, 4, 3, 6, 7, 5, 2, 8
4, 8, 6, 1, 5, 9, 7, 2, 3
8, 9, 1, 6, 3, 4, 7, 5, 2
8, 9, 6, 3, 5, 1, 7, 2, 4
7, 2, 8, 1, 6, 9, 5, 3, 4
9, 4, 1, 8, 5, 2, 3, 7, 6
7, 2, 1, 8, 6, 9, 5, 3, 4
1, 9, 3, 4, 6, 7, 5, 2, 8
1, 9, 4, 3, 6, 7, 2, 5, 8
9, 6, 2, 3, 5, 7, 1, 8, 4
7, 2, 8, 1, 6, 9, 3, 5, 4
9, 6, 3, 2, 5, 7, 1, 8, 4
9, 6, 2, 3, 5, 7, 8, 1, 4
7, 2, 3, 1, 5, 4, 8, 6, 9
7, 6, 9, 1, 5, 4, 8, 2, 3
9, 8, 4, 6, 5, 1, 7, 2, 3
9, 4, 8, 1, 5, 2, 3, 7, 6
7, 8, 2, 4, 5, 6, 9, 1, 3
8, 9, 6, 1, 3, 4, 5, 7, 2
9, 8, 4, 2, 5, 7, 6, 1, 3
4, 8, 6, 1, 5, 9, 2, 7, 3
9, 2, 1, 6, 5, 7, 4, 8, 3
8, 9, 1, 6, 3, 4, 5, 7, 2
7, 8, 2, 4, 5, 6, 1, 9, 3
5, 7, 3, 1, 4, 9, 2, 8, 6
4, 8, 1, 6, 5, 9, 7, 2, 3
7, 9, 3, 1, 2, 5, 8, 6, 4
9, 2, 6, 1, 5, 7, 8, 4, 3
7, 8, 2, 4, 3, 9, 5, 6, 1
5, 7, 1, 3, 4, 9, 2, 8, 6
7, 6, 1, 9, 5, 4, 8, 2, 3
9, 4, 1, 8, 5, 2, 7, 3, 6
9, 6, 3, 2, 5, 7, 8, 1, 4
9, 2, 1, 6, 5, 7, 8, 4, 3
9, 8, 2, 4, 5, 7, 1, 6, 3
9, 2, 6, 1, 5, 7, 4, 8, 3
9, 8, 4, 2, 5, 7, 1, 6, 3
9, 8, 4, 6, 5, 1, 2, 7, 3
1, 9, 3, 4, 6, 7, 2, 5, 8
7, 2, 1, 3, 5, 4, 6, 8, 9
7, 6, 9, 1, 5, 4, 2, 8, 3
9, 3, 1, 6, 5, 2, 7, 4, 8
9, 4, 8, 1, 5, 2, 7, 3, 6
7, 9, 1, 3, 2, 5, 8, 6, 4
8, 9, 3, 6, 5, 1, 7, 2, 4
7, 8, 4, 2, 5, 6, 1, 9, 3
7, 8, 4, 2, 3, 9, 5, 6, 1
7, 2, 1, 8, 6, 9, 3, 5, 4
4, 8, 1, 6, 5, 9, 2, 7, 3
9, 3, 1, 6, 5, 2, 4, 7, 8
9, 8, 6, 4, 5, 1, 2, 7, 3
7, 2, 3, 1, 5, 4, 6, 8, 9
7, 8, 4, 2, 3, 9, 6, 5, 1

Total answers: 72

vietnamese66.php

<?php
	/*
		Solve: __ + 13 * __ / __ / __ + 12 * __ - __ - 11 + __ * __ / __ == 66
		From:  http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/may/20/can-you-do-the-maths-puzzle-for-vietnamese-eight-year-olds-that-has-stumped-parents-and-teachers
		
		Thrown together in 15mins, pretty far from optimal
	*/

	ini_set('memory_limit', '512M'); // Told you

	function equals($a) {
		$result = $a[0] + 13 * $a[1] / $a[2] / $a[3] + 12 * $a[4] - $a[5] - 11 + $a[6] * $a[7] / $a[8];
		return $result;
	}
	
	function permutationCount($a) {
		$num = 1;
		$count = count($a);
		if ($count > 1) {
			for ($i = 1; $i <= $count; $i++) {
				$num *= $i;
			}
		}
		return $num;
	}
	
	$nums = [];
	for($i = 1; $i <= 9; $i++) {
		$nums[] = $i;
	}		
	
	$premutations = [];
	$premutationCount = permutationCount($nums);
	while(count($premutations) < $premutationCount) {
		shuffle($nums); // Hit it with a hammer until it works
		$hash = serialize($nums);
		if(!isset($premutations[$hash])) {
			$premutations[$hash] = $nums;
		}
	}
	
	$answers = [];
	foreach($premutations as $premutation) {
		$equals = equals($premutation);
		if($equals == 66) {
			$answers[] = $premutation;
		}
	}
	
	foreach($answers as $answer) {
		echo implode(', ', $answer) . "\n";
	}
	
	echo "\nTotal answers: ". count($answers);