def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
n, seen = x, set()
while n not in seen:
seen.add(n)
n = sum(int(d) ** 2 for d in str(n))
return n == 1 and len(seen) == 7
def mystery(x):
if not isinstance(x, str):
return False
if len(x) != 16:
return False
if not set(x).issubset('0123456789+*'):
return False
if sorted(c for c in x if c.isdigit()) != list('0123456789'):
return False
if x.count('+') != 4 or x.count('*') != 2:
return False
import re
if re.search(r'\b0\d', x):
return False
try:
return eval(x) == 2024
except Exception:
return False
def mystery(x):
import math
if not isinstance(x, int) or 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 (1000 <= x <= 9999):
return False
root = math.isqrt(x)
if root * root != x:
return False
if not is_prime(root):
return False
digit_sum = sum(int(d) for d in str(x))
ds_root = math.isqrt(digit_sum)
if ds_root * ds_root != digit_sum:
return False
rev_x = int(str(x)[::-1])
if not is_prime(rev_x):
return False
return True
def mystery(x):
if not isinstance(x, str):
return False
if len(x) > 25:
return False
if not set(x).issubset(set('12+*D-')):
return False
stack = []
for c in x:
if c == '1':
stack.append(1)
elif c == '2':
stack.append(2)
elif c == '+':
if len(stack) < 2:
return False
stack.append(stack.pop() + stack.pop())
elif c == '*':
if len(stack) < 2:
return False
stack.append(stack.pop() * stack.pop())
elif c == '-':
if len(stack) < 2:
return False
a = stack.pop()
b = stack.pop()
stack.append(b - a)
elif c == 'D':
if not stack:
return False
stack.append(stack[-1])
else:
return False
return len(stack) == 1 and stack[0] == 34359738371
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
s = str(x)
if len(s) != 4:
return False
# Gate A
n, d = x, 2
while d * d <= n:
if n % d == 0:
return False
d += 1 if d == 2 else 2
# Gate B
rep = bin(x)[2:]
if rep != rep[::-1]:
return False
# Gate C
sigma = sum(int(c) for c in s)
d = 2
while d * d <= sigma:
if sigma % d == 0:
return False
d += 1 if d == 2 else 2
return True
def mystery(x):
if not isinstance(x, str):
return False
if len(x) > 100:
return False
if not set(x).issubset({'L', 'R'}):
return False
p, q = 1, 1
for move in x:
if move == 'L':
p += q
elif move == 'R':
q += p
return p == 5225670 and q == 7489051
def mystery(x):
if not isinstance(x, int) or x <= 0:
return False
def is_prime(n):
if n < 2: return False
for i in range(2, int(n**0.5) + 1):
if n % i == 0: return False
return True
# Gate 1: x must be prime
if not is_prime(x):
return False
# Gate 2: decimal representation must be a palindrome
s = str(x)
if s != s[::-1]:
return False
# Gate 3: base-3 representation must also be a palindrome
n = x
digits = []
while n > 0:
digits.append(n % 3)
n //= 3
b3 = digits[::-1]
if b3 != b3[::-1]:
return False
# Gate 4: the length of the base-3 representation must be prime
if not is_prime(len(b3)):
return False
return True
def mystery(x):
if not isinstance(x, str):
return False
if len(x) != 80:
return False
if not set(x).issubset({'1', '2', '3'}):
return False
a, b, c = 1, 1, 1
for move in x:
if move == '1':
a = a + b + c
elif move == '2':
b = a + b + c
elif move == '3':
c = a + b + c
return a == 34467261 and b == 376513861 and c == 3155241
def mystery(x):
if not isinstance(x, str):
return False
if not all(c in 'AB' for c in x):
return False
if len(x) < 5 or len(x) > 30:
return False
a, b = 1, 1
for c in x:
if c == 'A':
a, b = a + b, b
else:
a, b = a, a + b
return a == 147 and b == 106
def mystery(x):
if not isinstance(x, str):
return False
# Must be reasonably short
if len(x) > 60:
return False
# No standard quine cheats or introspections
forbidden = ["eval", "exec", "import", "open", "read", "sys", "inspect", "__"]
if any(f in x for f in forbidden):
return False
try:
# x must evaluate to a callable (e.g., a lambda function)
func = eval(x)
# When called with no arguments, it must return its own source code
return func() == x
except Exception:
return False