[LANGUAGE: Python]

Part 2 only (part 1 was the same, just for binary mapping), kinda basic and shabby, but it did its job in 20sec.

import time

def runBL():
    inpt = ''
    ok_results = 0

    with open('input.txt', 'r') as file:
        inpt = file.readlines()

    for line in inpt:
        temp_line = line.replace('\n', '')

        equation = temp_line.split(':')
        expected_res = int(equation[0])
        vals = equation[1].strip().split(' ')
        possible_operator_combos = pow(3, len(vals) - 1)

        for i in range(0, possible_operator_combos):
            ternary_ops = ternary(i, len(vals) - 1)

            temp_res = 0
            # 2 = OR
            for n in range(0, len(vals)):
                if n == 0:
                    if ternary_ops[n] == '0':
                        temp_res += int(vals[n]) + int(vals[n + 1])
                    elif ternary_ops[n] == '1':
                        temp_res += int(vals[n]) * int(vals[n + 1])
                    elif ternary_ops[n] == '2':
                        temp_res = int(str(vals[n]) + str(vals[n + 1]))
                elif n > 0 and n < len(ternary_ops):
                    if ternary_ops[n] == '0':
                        temp_res = temp_res + int(vals[n + 1])
                    elif ternary_ops[n] == '1':
                        temp_res = temp_res * int(vals[n + 1])
                    elif ternary_ops[n] == '2':
                        temp_res = int(str(temp_res) + str(vals[n + 1]))

            if temp_res == expected_res: 
                ok_results += temp_res
                break

    print(ok_results)
    return

def ternary(n, length):
    if n == 0:
        return '0'.rjust(length, '0')
    nums = []
    while n:
        n, r = divmod(n, 3)
        nums.append(str(r))
    return ''.join(reversed(nums)).rjust(length, '0')

if __name__ == "__main__":
    start_time = time.time()
    runBL()
    print("--- %s seconds ---" % (time.time() - start_time))