Category: Correspondence

Question (EN): When 1/4×1/8=1/(4×A)=1/B, what is the sum of A and B?
Question (KO): 1/4×1/8=1/(4×A)=1/B 일 때 A와 B의 합은?

Answer: 40

Solution (Python):
var_a = '1/4×1/8=1/(4×A)=1/B'
var_b = 'A'
ans_dict = dict()
var_a = var_a.replace('×','*')
var_a = var_a.replace('x','*')
var_a = var_a.replace('÷','/')
variable_candi = set(['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'])
for v in set(var_a):
    if v in variable_candi:
        ans_dict[v] = 0
candidate_num = [i for i in range(51)]
candi = list(itertools.product(candidate_num, repeat=len(ans_dict)))
for c in candi:
    temp = var_a
    for i, (k, _) in enumerate(ans_dict.items()):
        temp = temp.replace(k, str(c[i]))
    term_list = []
    op_list = []
    temp_c = ''
    for tc in temp:
        if tc not in '+-*/=><().':
            temp_c += tc
        else:
            op_list.append(tc)
            term_list.append(temp_c)
            temp_c = ''
    term_list.append(temp_c)
    new_eq = ''
    for i in range(len(op_list)):
        if term_list[i] == '':
            new_eq += str(term_list[i])+op_list[i]
        else:
            new_eq += str(int(term_list[i]))+op_list[i]
    new_eq += str(int(term_list[-1]))
    new_eq=new_eq.replace('=', '==')
    new_eq=new_eq.replace('>==', '>=')
    new_eq=new_eq.replace('<==', '<=')
    eval_result = False
    try:
        if '=' in new_eq and '>' not in new_eq and '<' not in new_eq:
            new_eq=new_eq.replace('==','=')
            new_eq=new_eq.replace('>','')
            new_eq=new_eq.replace('<','')
            new_eq=new_eq.split('=')
            for i in range(len(new_eq)-1):
                eval_result = math.isclose(eval(new_eq[i]), eval(new_eq[i+1]))
                if not eval_result:
                    break
        else:
            eval_result = eval(new_eq)
    except:
        eval_result = False
        pass
    if eval_result:
        for i, (k, _) in enumerate(ans_dict.items()):
            ans_dict[k] = int(c[i])
var_c = ans_dict[var_b]
var_d = '1/4×1/8=1/(4×A)=1/B'
var_e = 'B'
ans_dict = dict()
var_d = var_d.replace('×','*')
var_d = var_d.replace('x','*')
var_d = var_d.replace('÷','/')
variable_candi = set(['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'])
for v in set(var_d):
    if v in variable_candi:
        ans_dict[v] = 0
candidate_num = [i for i in range(51)]
candi = list(itertools.product(candidate_num, repeat=len(ans_dict)))
for c in candi:
    temp = var_d
    for i, (k, _) in enumerate(ans_dict.items()):
        temp = temp.replace(k, str(c[i]))
    term_list = []
    op_list = []
    temp_c = ''
    for tc in temp:
        if tc not in '+-*/=><().':
            temp_c += tc
        else:
            op_list.append(tc)
            term_list.append(temp_c)
            temp_c = ''
    term_list.append(temp_c)
    new_eq = ''
    for i in range(len(op_list)):
        if term_list[i] == '':
            new_eq += str(term_list[i])+op_list[i]
        else:
            new_eq += str(int(term_list[i]))+op_list[i]
    new_eq += str(int(term_list[-1]))
    new_eq=new_eq.replace('=', '==')
    new_eq=new_eq.replace('>==', '>=')
    new_eq=new_eq.replace('<==', '<=')
    eval_result = False
    try:
        if '=' in new_eq and '>' not in new_eq and '<' not in new_eq:
            new_eq=new_eq.replace('==','=')
            new_eq=new_eq.replace('>','')
            new_eq=new_eq.replace('<','')
            new_eq=new_eq.split('=')
            for i in range(len(new_eq)-1):
                eval_result = math.isclose(eval(new_eq[i]), eval(new_eq[i+1]))
                if not eval_result:
                    break
        else:
            eval_result = eval(new_eq)
    except:
        eval_result = False
        pass
    if eval_result:
        for i, (k, _) in enumerate(ans_dict.items()):
            ans_dict[k] = int(c[i])
var_f = ans_dict[var_e]
var_g = var_c + var_f
print(int(var_g))