a = [1,4,5,10]
cache = {}
for i in a:
    cache[i] = 1

counter = 0
def coin(x):
   if not x in cache:
        tmp = []
        for i in a:
            if (x-i) > 0:
                if (x-i) in cache:
                    tmp.append(1+cache[x-i])
                else:
                    tmp.append(1+coin(x-i))
        cache[x] = min(tmp)
        return cache[x]
    else:
        return cache[x]