Python-Code

cent = 100
d  = [cent]
lc = [10, 5, 2, 1] 
kombinationen = []
n = 0


def kombi(li,c):
    ko = []
    for e in li:
        while e <= c:
            ko.append(e)
            c -= e
    return ko

def xxx(d): 
    global n
    global cent
    p = d[:]
    p.reverse()
    e = p[n]     
    
    if e > 1: 
        i = lc.index(e) + 1
        p.remove(e)      
        for j in range(2):
            p.append(lc[i])
        if sum(p) < cent:
            p.append(1)
        sr(p)
        if p not in kombinationen:
            kombinationen.append(p)
        xxx(p) 
    
    sr(p)    
    if e == 1 :
        if n < len(p)-1:
            n += 1
            xxx(p)     


def sr(s):
    s.sort(); s.reverse()


# Start
d = kombi(lc,cent)
kombinationen.append(d)  
xxx(d)


# Fehlende hinzufügen
sr(kombinationen)
for e in kombinationen: 
    if len(e) > 1:   
        p = e[:]
        if (p[-1] == 1 and p[-2] == 1) :
            del p[-1]; del p[-1]
            p.append(2)
            sr(p)
            if p not in kombinationen:
                if sum(p) == cent:
                    kombinationen.append(p)            

sr(kombinationen)
for e in kombinationen: 
    if len(e) > 1:   
        p = e[:]
        if (p[0] > p[1] and p[1] != 1 and p[2] == 1):
            del p[1]
            p.append(1); p.append(1)            
            sr(p)
            if p not in kombinationen: 
                if sum(p) == cent:
                    kombinationen.append(p) 
                    
sr(kombinationen)
if kombinationen[-1][0] == 2:
    p = kombinationen[-1][:]
    del p[0]
    p.append(1); p.append(1)
    sr(p)
    kombinationen.append(p) 


# Doppelte ausfiltern
k = []
for e in kombinationen:
    if e not in k:
        k.append(e)


# Ausgabe
sr(k)
for e in k:
    print(e)
print('Anzahl der Kombinationen:', len(k))