Dragon simulator

counter.php

<?php 

$allFollowingPieces = array(
    'a' => array('b', 'E'),
    'b' => array('c', 'D'),
    'c' => array('d', 'C'),
    'd' => array('e', 'B'),
    'e' => array('a', 'A'),
    'A' => array('B', 'e'),
    'B' => array('C', 'd'),
    'C' => array('D', 'c'),
    'D' => array('E', 'b'),
    'E' => array('A', 'a'),
);

$pieces = array();

$steps = 25;
$pieces_number = $steps/5;
$count = 0;

for ($i=0; $i <= $pieces_number; $i++) { 
    $pieces['a'] = $pieces_number - $i;
    $pieces['b'] = $pieces_number - $i;
    $pieces['c'] = $pieces_number - $i;
    $pieces['d'] = $pieces_number - $i;
    $pieces['e'] = $pieces_number - $i;
    $pieces['A'] = $i;
    $pieces['B'] = $i;
    $pieces['C'] = $i;
    $pieces['D'] = $i;
    $pieces['E'] = $i;

    $lastPiece = 'e';
    $solution = array();

    $count = putPiece($lastPiece, $pieces, $allFollowingPieces, $solution, $count);
}

echo $count . PHP_EOL;

function putPiece($lastPiece, $pieces, $allFollowingPieces, $solution, $count) {
    if (array_sum($pieces) == 0) {
        //echo implode(', ', $solution).PHP_EOL;
        $count++;
    } else {
        $followingPieces = $allFollowingPieces[$lastPiece];

        foreach ($followingPieces as $followingPiece) {
            if ($pieces[$followingPiece] > 0) {
                $newPieces = $pieces;
                $newPieces[$followingPiece] = $pieces[$followingPiece] - 1;
                $newSolution = $solution;
                $newSolution[] = $followingPiece;
                $count = putPiece($followingPiece, $newPieces, $allFollowingPieces, $newSolution, $count);
            }     
        }
    }

    return $count;
}