def mystery(x):
try:
s = str(x)
except:
return False
if len(s) < 3:
return False
temp = [ord(c) for c in s]
sum_temp = sum(temp)
if sum_temp % 10 != 0:
return False
product = 1
for t in temp:
if t == 0:
product = 0
break
product *= (t % 10)
if product == 0:
return False
# Additional confusing computation
rev_temp = temp[::-1]
diff_sum = sum(abs(temp[i] - rev_temp[i]) for i in range(len(temp)))
if diff_sum % 2 != 0:
return False
return all(s[i] == s[-1 - i] for i in range(len(s) // 2))
def mystery(x):
try:
s = str(x)
except:
return False
if s.startswith('-'):
s = s[1:]
if len(s) < 2:
return False
# Check uniqueness of digits
if len(s) != len(set(s)):
return False
# Check alternation of digit parity
is_odd = lambda c: int(c) % 2 == 1
for i in range(len(s) - 1):
if is_odd(s[i]) == is_odd(s[i+1]):
return False
# Check sum divisibility
if sum(int(d) for d in s) % 3 != 0:
return False
# Check first digit constraint
if int(s[0]) >= 8:
return False
# Check last digit constraint
if s[-1] in ['0', '1']:
return False
return True
def mystery(x):
try:
s = str(x).lower().strip()
except:
return False
if not all(c.isalpha() for c in s):
return False
if len(s) < 3 or len(s) % 2 == 0:
return False
# Confusing: compute sum ord
ords = [ord(c) for c in s]
total = sum(ords)
if total % 7 != 0:
return False
# Product of (ord - ord('a') +1)
prod = 1
for o in ords:
d = o - ord('a') + 1
prod *= d
if prod > 10000:
prod = 0
break
if prod == 0 or prod % 5 != 0:
return False
# More confusion: reverse ords sum diff even
rev_ords = ords[::-1]
diff = sum(abs(ords[i] - rev_ords[i]) for i in range(len(ords)))
if diff % 2 != 0:
return False
# Finally, the key condition hidden among the noise
return s == s[::-1]
def mystery(x):
from collections import Counter
try:
s = str(x)
except:
return False
if s.startswith('-'):
s = s[1:]
if len(s) < 2:
return False
num = int(s)
power = len(s)
armstrong_sum = sum(int(d) ** power for d in s)
if armstrong_sum != num:
return False
digit_sum = sum(int(d) for d in s)
if digit_sum % 2 != 0:
return False
digit_counts = Counter(s)
if any(count > 2 for count in digit_counts.values()):
return False
return True
def mystery(x):
try:
s = str(x).strip()
except:
return False
if s.startswith('-'):
return False
if not s.isdigit() or len(s) < 3:
return False
digits = [int(c) for c in s]
if len(set(s)) != len(s):
return False
sum_d = sum(digits)
if sum_d % 3 != 0:
return False
prod = 1
for d in digits:
prod *= d
if prod == 0:
break
if prod == 0 or prod % 7 != 0:
return False
# Confusing: check sum of squares modulo 11
sum_sq = sum(d ** 2 for d in digits)
if sum_sq % 11 != 0:
return False
# More confusion: alternating sum parity
alt_sum = sum(digits[i] * (1 if i % 2 == 0 else -1) for i in range(len(digits)))
if alt_sum % 2 != 0:
return False
# Useless computation to distract
rev_digits = digits[::-1]
diff_prod = 1
for i in range(len(digits)):
diff = abs(digits[i] - rev_digits[i])
diff_prod *= (diff + 1)
if diff_prod % 5 == 0:
return False # Actually filters some, but for our solution it's ok
n = int(s)
from math import sqrt
root = int(sqrt(n) + 0.5)
if root * root != n:
return False
return True
def mystery(x):
try:
s = str(x).strip()
except:
return False
if s.startswith('-'):
return False
if not s.isdigit() or len(s) < 2:
return False
n = int(s)
digits = [int(c) for c in s]
# Red herring: sum of digits must be odd
if sum(digits) % 2 == 0:
return False
# Red herring: no zeros allowed
if 0 in digits:
return False
# Red herring: all digits must be unique
if len(set(digits)) != len(digits):
return False
# Red herring: product of digits divisible by 3
product = 1
for d in digits:
product *= d
if product % 3 != 0:
return False
# Red herring: first digit constraint
if digits[0] >= 5:
return False
# Red herring: last digit constraint
if digits[-1] <= 3:
return False
# Red herring: product modulo check
if product % 7 == 0:
return False
# Core condition: each digit raised to consecutive powers (1, 2, 3, ...)
calculated = sum(d ** (i + 1) for i, d in enumerate(digits))
return calculated == n
def mystery(x):
try:
s = str(x).strip()
except:
return False
if s.startswith('-') or not s.isdigit() or len(s) < 3:
return False
digits = [int(c) for c in s]
if 0 in digits:
return False
if len(set(s)) != len(s):
return False
if sum(digits) % 9 != 0:
return False
prod = 1
for d in digits:
prod *= d
if prod % 16 != 0:
return False
alt = sum(digits[i] * (1 if i % 2 == 0 else -1) for i in range(len(digits)))
if alt % 2 != 0:
return False
sum_sq = sum(d ** 2 for d in digits)
if sum_sq % 5 != 3:
return False
rev = digits[::-1]
diff_sum = sum(abs(digits[i] - rev[i]) for i in range(len(digits)))
if diff_sum % 2 != 0:
return False
# Confusing computation: sum of cubes modulo something
sum_cubes = sum(d ** 3 for d in digits)
if sum_cubes % 13 != 6:
return False
# More distraction: check if product of (d + i) or similar
pos_prod = 1
for i, d in enumerate(digits):
pos_prod *= (d + i + 1)
if pos_prod % 7 == 0:
return False
n = int(s)
# Hidden key condition
root = round(n ** (1 / 3))
return root ** 3 == n
def mystery(x):
try:
s = str(x).strip()
except:
return False
if s.startswith('-') or not s.isdigit() or len(s) < 3:
return False
n = int(s)
digits = [int(c) for c in s]
# Red herring: sum must be divisible by 3
if sum(digits) % 3 != 0:
return False
# Red herring: no repeated digits
if len(set(digits)) != len(digits):
return False
# Red herring: product of digits must be even
product = 1
for d in digits:
product *= d
if product % 2 != 0:
return False
# Red herring: first digit must be odd
if digits[0] % 2 == 0:
return False
# Red herring: last digit must be even
if digits[-1] % 2 == 1:
return False
# Red herring: alternating sum must be positive
alt_sum = sum(digits[i] * (1 if i % 2 == 0 else -1) for i in range(len(digits)))
if alt_sum <= 0:
return False
# Red herring: sum of squares must be odd
sum_sq = sum(d ** 2 for d in digits)
if sum_sq % 2 == 0:
return False
# Core condition: no zeros allowed
if 0 in digits:
return False
# Core condition: each digit must divide the number
for d in digits:
if n % d != 0:
return False
return True
def mystery(x):
try:
s = str(x).strip()
except:
return False
if s.startswith('-') or not s.isdigit() or len(s) < 3:
return False
digits = [int(c) for c in s]
n = int(s)
# Red herring: sum of digits modulo 5
if sum(digits) % 5 != 0:
return False
# Red herring: no zeros
if 0 in digits:
return False
# Red herring: all unique digits
if len(set(s)) != len(s):
return False
# Red herring: first digit odd
if digits[0] % 2 == 0:
return False
# Red herring: last digit odd
if digits[-1] % 2 == 0:
return False
# Red herring: product of digits modulo 4
product = 1
for d in digits:
product *= d
if product % 4 != 0:
return False
# Red herring: sum of squares modulo 6
sum_sq = sum(d ** 2 for d in digits)
if sum_sq % 6 != 0:
return False
# Red herring: alternating sum even
alt_sum = sum(digits[i] * (1 if i % 2 == 0 else -1) for i in range(len(digits)))
if alt_sum % 2 != 0:
return False
# Red herring: differences with reverse even sum
rev_digits = digits[::-1]
diff_sum = sum(abs(digits[i] - rev_digits[i]) for i in range(len(digits)))
if diff_sum % 2 != 0:
return False
# More distraction: Armstrong-like sum modulo 13
power = len(s)
arm_sum = sum(d ** power for d in digits)
if arm_sum % 13 != 8:
return False
# Additional confusion: product of (d + 1) modulo 7
pos_prod = 1
for d in digits:
pos_prod *= (d + 1)
if pos_prod % 7 == 0:
return False
# Core condition: sum of factorials of digits equals n
def factorial(k):
if k == 0 or k == 1:
return 1
res = 1
for i in range(2, k + 1):
res *= i
return res
fact_sum = sum(factorial(d) for d in digits)
return fact_sum == n
def mystery(x):
try:
s = str(x).strip()
except:
return False
if s.startswith('-') or not s.isdigit() or len(s) < 3:
return False
n = int(s)
digits = [int(c) for c in s]
# Red herring: sum of digits must be divisible by 3
if sum(digits) % 3 != 0:
return False
# Red herring: product of digits must be nonzero
product = 1
for d in digits:
product *= d
if product == 0:
return False
# Red herring: sum of squares modulo 8
sum_sq = sum(d ** 2 for d in digits)
if sum_sq % 8 != 6:
return False
# Red herring: alternating sum must be even
alt_sum = sum(digits[i] * (1 if i % 2 == 0 else -1) for i in range(len(digits)))
if alt_sum % 2 != 0:
return False
# Red herring: no digit should be 0
if 0 in digits:
return False
# Red herring: first digit must be less than 8
if digits[0] >= 8:
return False
# Red herring: sum of cubes modulo 13
sum_cubes = sum(d ** 3 for d in digits)
if sum_cubes % 13 != 1:
return False
# Red herring: maximum digit should be at least 5
if max(digits) < 5:
return False
# Red herring: last digit must be odd
if digits[-1] % 2 == 0:
return False
# Red herring: digit frequency check
from collections import Counter
freq = Counter(digits)
if any(count > 2 for count in freq.values()):
return False
# Core condition: Kaprekar number
# A number whose square can be split into two parts that sum to the original number
square = n * n
square_str = str(square)
for i in range(1, len(square_str)):
left_part = square_str[:i]
right_part = square_str[i:]
left_num = int(left_part)
right_num = int(right_part) if right_part else 0
if left_num + right_num == n:
return True
return False