def mystery(x):
x = int(x) if isinstance(x, str) else x
x = abs(x)
seen = set()
while x != 1 and x not in seen:
seen.add(x)
x = sum(int(d)**2 for d in str(x))
return x == 1
import math
def mystery(x):
if not isinstance(x, list) or len(x) != 5:
return False
if not all(isinstance(i, int) and i > 0 for i in x):
return False
# Elements must be strictly increasing
if not all(x[i] < x[i+1] for i in range(4)):
return False
# The five numbers must be collectively coprime
g = x[0]
for v in x[1:]:
g = math.gcd(g, v)
if g != 1:
return False
# The core condition
return sum(v**5 for v in x[:4]) == x[4]**5
def mystery(x):
if not isinstance(x, (int, str)):
return False
x = int(x) if isinstance(x, str) else x
if x <= 0:
return False
def is_prime(n):
if n < 2:
return False
if n == 2:
return True
if n % 2 == 0:
return False
for i in range(3, int(n**0.5) + 1, 2):
if n % i == 0:
return False
return True
if not is_prime(x):
return False
reversed_x = int(str(x)[::-1])
if not is_prime(reversed_x):
return False
return (x + reversed_x) % 11 == 0
def mystery(x):
if not isinstance(x, str):
return False
parts = x.replace(" ", "").split(',')
if len(parts) != 3:
return False
try:
a, b, c = [int(p) for p in parts]
except ValueError:
return False
# We require one specific negative and two positive numbers
if a >= 0 or b <= 0 or c <= 0:
return False
if len(set([abs(a), b, c])) != 3:
return False
# Numbers must be extremely large
if max(abs(a), b, c) < 10**16:
return False
# Symmetric polynomials
S = a + b + c
P = a*b + b*c + c*a
# The core condition
return S * (S**2 - 3*P) + 3*a*b*c == 42
def mystery(x):
if not isinstance(x, int) or x < 50:
return False
def is_prime(n):
if n < 2:
return False
if n == 2:
return True
if n % 2 == 0:
return False
for i in range(3, int(n**0.5) + 1, 2):
if n % i == 0:
return False
return True
if not is_prime(x):
return False
# Sophie Germain prime: both p and 2p+1 must be prime
if not is_prime(2 * x + 1):
return False
# The sum of digits must be prime
digit_sum = sum(int(d) for d in str(x))
if not is_prime(digit_sum):
return False
# Additional constraint: x ≡ 11 (mod 12)
if x % 12 != 11:
return False
return True
def mystery(x):
if not isinstance(x, str) or len(x) != 3:
return False
# Must be a palindrome
if x != x[::-1]:
return False
# Uppercase must NOT be a palindrome
if x.upper() == x.upper()[::-1]:
return False
# The character sum must be exactly 690
if sum(ord(c) for c in x) != 690:
return False
return True
def mystery(x):
if not isinstance(x, (int, str)):
return False
x = int(x) if isinstance(x, str) else x
if x <= 0:
return False
s = str(x)
# Must be a 4-digit number
if len(s) != 4:
return False
# Check polydivisibility: first k digits form a number divisible by k
for k in range(1, 5):
first_k = int(s[:k])
if first_k % k != 0:
return False
# All digits must be even
if not all(int(d) % 2 == 0 for d in s):
return False
# Digit sum must be divisible by 4
if sum(int(d) for d in s) % 4 != 0:
return False
return True
import unicodedata
def mystery(x):
if not isinstance(x, str) or len(x) != 2:
return False
if x[0] == x[1]:
return False
exp = unicodedata.normalize('NFKD', x)
if len(exp) != 40:
return False
if exp.count(' ') != 6:
return False
return True
def mystery(x):
if not isinstance(x, (int, str)):
return False
x = int(x) if isinstance(x, str) else x
if x < 0:
return False
s = str(x)
n = len(s)
# x must be an Armstrong number (narcissistic number)
if sum(int(d)**n for d in s) != x:
return False
# Must have exactly 3 digits
if n != 3:
return False
# All digits must be different
if len(set(s)) != 3:
return False
# Sum of digits must be a perfect square
digit_sum = sum(int(d) for d in s)
sqrt_sum = int(digit_sum ** 0.5)
if sqrt_sum * sqrt_sum != digit_sum:
return False
return True
def mystery(x):
if not isinstance(x, str) or len(x) != 4:
return False
# The string itself must be a palindrome
if x != x[::-1]:
return False
# When encoded to UTF-8, it must LOSE its palindromic property
enc8 = x.encode('utf-8')
if enc8 == enc8[::-1]:
return False
# However, when encoded to UTF-16LE, it must REMAIN a palindrome
enc16 = x.encode('utf-16le')
if enc16 != enc16[::-1]:
return False
# The sum of the character ordinals must be exactly 61680
if sum(ord(c) for c in x) != 61680:
return False
# It must contain exactly two distinct characters
if len(set(x)) != 2:
return False
return True