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 0x1,2x11,1x12,0x13,0x15,0x20  Total: 3
 1x1,0x11,0x12,1x13,0x15,1x20  Total: 3
 1x1,3x11,0x12,0x13,0x15,0x20  Total: 4
 2x1,0x11,1x12,0x13,0x15,1x20  Total: 4
 3x1,1x11,0x12,0x13,0x15,1x20  Total: 5
 4x1,0x11,0x12,0x13,2x15,0x20  Total: 6
 6x1,0x11,0x12,1x13,1x15,0x20  Total: 8
 7x1,0x11,1x12,0x13,1x15,0x20  Total: 9
 8x1,0x11,0x12,2x13,0x15,0x20  Total: 10
 8x1,1x11,0x12,0x13,1x15,0x20  Total: 10
 9x1,0x11,1x12,1x13,0x15,0x20  Total: 11
10x1,0x11,2x12,0x13,0x15,0x20  Total: 12
10x1,1x11,0x12,1x13,0x15,0x20  Total: 12
11x1,1x11,1x12,0x13,0x15,0x20  Total: 13
12x1,2x11,0x12,0x13,0x15,0x20  Total: 14
14x1,0x11,0x12,0x13,0x15,1x20  Total: 15
19x1,0x11,0x12,0x13,1x15,0x20  Total: 20
21x1,0x11,0x12,1x13,0x15,0x20  Total: 22
22x1,0x11,1x12,0x13,0x15,0x20  Total: 23
23x1,1x11,0x12,0x13,0x15,0x20  Total: 24
34x1,0x11,0x12,0x13,0x15,0x20  Total: 34                    

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procedure muenze(a,b,c,d,e,f:integer)//hier sind die variablen die zurückgegeben werden
begin
  dann kommt hier dein ganzer quellcode;
  muenze(a,b,c,d,e,f);//damit ruft sich die prozedur selbst auf...et voila du hast eine rekursion
end;                    

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34 cent
münzen: 20,15,13,12,11,1

1. Vergleich
(34 - 20 (14)) > 0 --> 1. Münze ist 20, rest ist 14

2. Vergleich
(14 - 20 (-6)) > 0 --> nächste Münze
(14 - 15 (-1)) > 0 --> nächste Münze
(14 - 13 (1))  > 0 --> 2. Münze ist 13, rest ist 1

3. Vergleich
...
(1 - 1 (0))    = 0 --> 3. Münze ist 1, rest ist 0 --> Beenden                    

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<?php

$coins = array(1,11,12,13,15,20);

$value = 78;

$minsolution = array();

$stack = array(array());

while(count($stack)) {
    $tmp = array_shift($stack);

    $tmpsum = array_sum($tmp);

    if ($tmpsum == $value) {
        $minsolution = $tmp;
        break;
    }

    if ($tmpsum > $value) {
        continue;
    }

    foreach($coins as $newcoin) {
        $newtmp = $tmp;
        $newtmp[] = $newcoin;
        $stack[] = $newtmp;
    }
}

var_dump($minsolution);
echo array_sum($minsolution);

?>