def evaluate (method,running_sum):
    if eval(method) == target:
        if method not in list_methods:
            list_methods.append(method)
            print (f'Eval: {method}')
        return True
    if running_sum == target:
        if method not in list_methods:
            list_methods.append(method)
            print (f'Running sum: {method}')
        return True

def new_total (total,item,operation):
    if operation == "+": return total + item
    if operation == "-": return total - item
    if operation == "*" and total !=0:
        return total * item
    else:
        return ""
    if operation == "/" and total !=0 and item != 0:
        return total / item
    else:
        return ""

def solve (array,total=0,method="",list_method=[]):
    if len(array) == 0:
        return

    for (index,item) in enumerate(array):
        #Set methods and totals to "":
        add_method, sub_method, mul_method, div_method = "", "", "", ""
        add_total, sub_total, mul_total, div_total = 0, 0, 0,0

        #Assign methods and totals to a list:
        methods = [add_method, sub_method, mul_method, div_method]
        totals = [add_total, sub_total, mul_total, div_total]
        str_func = ["+", "-", "*", "/"]

        #Create new array
        remaining = array[:index] + array[index+1:]

        for index_1 in range (len(methods)):
            if method != "":
                methods[index_1] = method + str_func[index_1] + str(array[index])
                totals[index_1] = new_total(total,item,str_func[index_1])
            else:
                methods[index_1] = method + str(array[index])
                totals[index_1] = new_total(total,item,str_func[index_1])
                break

        for index_2 in range (len(methods)):
            try:
                if evaluate(methods[index_2], totals[index_2]):
                    return
            except Exception:
                pass

        for index_3 in range (len(methods)):
            try:
                solve(remaining, total= totals[index_3],method= methods[index_3])
            except Exception:
                pass


array = [100,9,10,40,1,3]
target = 940
print (f'Solutions for {array} to reach {target}')
list_methods = []
solve(array)
if list_methods == []: print ("None")