Math game solver

This is a script designed to run a list of arithmetic functions. It is for a math game where one rolls 3 dice to get a number then roll them again to get 3 numbers that using roots, multiplication, addition, subtraction, division, and exponents. When I input the numbers I get back a blank page. Thanks to all who help.

<?php 
	$functions = array(
		"$a+$b+$c", 
		"$a+$b-$c", 
		"$a+$b*$c", 
		"$a+$b/$c",
		"$a+$b^(1/$c)",
		"$a+$b^$c",
		"$a+^($b+$c)",
		"$a+^($b-$c)",
		"$a+^($a*$c)",
		"$a+^($b/$c)",
		"$a+^($b^(1/$c))",
		"$a+^($b^$c)",
		"$a+^(1/($b+$c))",
		"$a+^(1/($b-$c))",
		"$a+^(1/($a*$c))",
		"$a+^(1/($b/$c))",
		"$a+^(1/($b^(1/$c)))",
		"$a+^(1/($a^$c))");
		
	if(!$_POST['A'])
    {
		?>
       	<form action="<?php $_SERVER['PHP_SELF']; ?>" method="post">
        Target:<input name="Target" type="text" size="20" maxlength="4">
        Number 1:<input name="A" type="text" size="20" maxlength="2">
        Number 2:<input name="B" type="text" size="20" maxlength="2">
        Number 3:<input name="C" type="text" size="20" maxlength="2">
        <input type="submit" name="Send" value="submit">
        </form>
        <?php
    }
	else
    {
		$target = $_POST['Target'];
    	$a = $_POST['A'];
		$b = $_POST['B'];
		$c = $_POST['C'];
		
		$nums = array(brute($a, $b, $c));
		array_push ($num, brute($a, $c, $b));
		array_push ($num, brute($b, $a, $c));
		array_push ($num, brute($b, $c, $a));
		array_push ($num, brute($c, $a, $b));
		array_push ($num, brute($c, $b, $a));
		
		$results = compare($nums, $target);
		
		while (list($pos, $result) = each($results))
			{
				echo($result['result']);
				echo($result['function']);
			}	
    }

	function brute($a, $b, $c)
	{
		$array = array();
		while(list($pos, $function) = each($functions))
		{
			$array2 = array
			(
			"result"=>sprintf($function),
			"function"=>$function
			);
			array_push($array, $array2);
		}
		
		return($array);
	}
	function compare($arrays, $target)
	{
		
			while(list($pos, $array)= each($arrays))
			{
				$diffs = array();
				array_push($diffs, $target - $array['result']);
				
			}
			$mins = min(diffs);
			
			while (list($pos, $min) = each( $mins))
			{	
				$results = array();
				while (list($pos, $diff)= each($diffs))
				{
					if ($min = $diff['result'])
					{
						array_push($results, $diff);
					}
				}
			}
			
			return ($results);
	}

i fixed it

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