2018 年刑偵科推理試題

tuili.py

#!/usr/bin/env python3

# 題目: https://imgur.com/a/WvVHKUO

import string

base = 4
digs = string.digits + string.ascii_letters
N = 4 ** 10


def to_base4(n):
    digits = []
    while n:
        digits.append(digs[int(n % base)])
        n = int(n / base)
    if len(digits) < 10:
        digits += ['0'] * (10 - len(digits))
    digits.reverse()
    return digits


def base4_to_abcd(digits):
    return [chr(65+int(x)) for x in digits]


def check_1(ans):
    # 本題 always true
    return True


def check_2(ans):
    if (ans[1] == 'A' and ans[4] == 'C'):
        return True
    if (ans[1] == 'B' and ans[4] == 'D'):
        return True
    if (ans[1] == 'C' and ans[4] == 'A'):
        return True
    if (ans[1] == 'D' and ans[4] == 'B'):
        return True
    return False


def check_3(ans):
    if (ans[2] == 'A'):
        return (ans[5] != ans[2]) and (ans[5] == ans[1]) and (ans[5] == ans[3])
    if (ans[2] == 'B'):
        return (ans[2] != ans[5]) and (ans[2] == ans[1]) and (ans[2] == ans[3])
    if (ans[2] == 'C'):
        return (ans[2] != ans[1]) and (ans[2] == ans[5]) and (ans[2] == ans[3])
    if (ans[2] == 'D'):
        return (ans[2] != ans[3]) and (ans[2] == ans[5]) and (ans[5] == ans[1])


def check_4(ans):
    # 未排除多選成立情況
    if (ans[3] == 'A'):
        return ans[0] == ans[4]
    if (ans[3] == 'B'):
        return ans[1] == ans[6]
    if (ans[3] == 'C'):
        return ans[0] == ans[8]
    if (ans[3] == 'D'):
        return ans[5] == ans[9]


def check_5(ans):
    if (ans[4] == 'A'):
        return (ans[7] == 'A' and ans[3] != 'A' and ans[8] != 'A' and ans[6] != 'A')
    if (ans[4] == 'B'):
        return (ans[7] != 'B' and ans[3] == 'B' and ans[8] != 'B' and ans[6] != 'B')
    if (ans[4] == 'C'):
        return (ans[7] != 'C' and ans[3] != 'C' and ans[8] == 'C' and ans[6] != 'C')
    if (ans[4] == 'D'):
        return (ans[7] != 'D' and ans[3] != 'D' and ans[8] != 'D' and ans[6] == 'D')


def check_6(ans):
    # 未排除多選成立情況
    if (ans[5] == 'A'):
        return (ans[7] == ans[1] and ans[7] == ans[3])
    if (ans[5] == 'B'):
        return (ans[7] == ans[0] and ans[7] == ans[5])
    if (ans[5] == 'C'):
        return (ans[7] == ans[2] and ans[7] == ans[9])
    if (ans[5] == 'D'):
        return (ans[7] == ans[4] and ans[7] == ans[8])


def check_7(ans, selected_count):
    idx = selected_count.index(min(selected_count))
    return (ans[6] == 'A' and idx == 2) or (ans[6] == 'B' and idx == 1) or (ans[6] == 'C' and idx == 0) or (ans[6] == 'D' and idx == 3)


def check_8(ans):
    return True


def check_9(ans):
    return True


def check_10(ans, selected_count):
    delta = max(selected_count) - min(selected_count)
    return (ans[9] == 'A' and delta == 3) or (ans[9] == 'B' and delta == 2) or (ans[9] == 'C' and delta == 4) or (ans[9] == 'D' and delta == 1)


def check(ans):
    if not check_2(ans):
        return False
    if not check_5(ans):
        return False
    if not check_6(ans):
        return False
    if not check_3(ans):
        return False
    # 上述四個條件下來，剩下 120 組
    if not check_4(ans):
        return False
    # 上述五個條件下來，剩下 12 組
    selected_count = [ans.count(x) for x in ['A', 'B', 'C', 'D']]
    if not check_7(ans, selected_count):
        return False
    # 上述六個條件下來，剩下 2 組
    if not check_10(ans, selected_count):
        return False
    # 上述七個條件下來，剩下以下 2 組 (這題白做工)
    # ----------------------------------------
    # ['B', 'C', 'A', 'C', 'A', 'C', 'D', 'A', 'B', 'A']
    # ['D', 'C', 'A', 'C', 'A', 'C', 'B', 'A', 'D', 'A']
    # total: 2
    # ----------------------------------------
    # 剩下兩組，乾脆就直接用推的:
    # 還有 8, 9 兩題, 兩組中 8 的答案一樣，從 9 去看
    return True


count = 0
for i in range(N):
    d = to_base4(i)
    ans = base4_to_abcd(d)
    if check(ans):
        print(ans)
        count += 1
print("total:", count)