def mystery(x):
if type(x) is not int:
return False
if x <= 0:
return False
n = int(
"1"
+ "0" * 126
+ "3039"
+ "0" * 17
+ "10933"
+ "0" * 122
+ "31f49c5b",
16,
)
return (
x.bit_length() == 521
and x.bit_count() == 7
and n % x == 0
)
def mystery(x):
if type(x) is not str:
return False
if len(x) > 54:
return False
# No digits, no quotes, no spaces, no dots, no underscores.
bad_chars = set('0123456789"\'. _\n\t')
if any(c in x for c in bad_chars):
return False
try:
# Evaluate in an empty environment (no built-ins like `len`, `int`, `str`, `abs`, etc.)
res = eval(x, {"__builtins__": None}, {})
return res == 1337
except Exception:
return False
def mystery(x):
if type(x) is not str:
return False
if len(x) != 56:
return False
if not all(97 <= ord(c) <= 122 for c in x):
return False
import hashlib
y = bytes(219 - ord(c) for c in reversed(x))
target = bytes.fromhex(
"248d6a61d20638b8e5c026930c3e6039a33ce45964ff2167f6ecedd419db06c1"
)
return hashlib.sha256(y).digest() == target
def mystery(x):
if type(x) is not str:
return False
parts = x.split(',')
if len(parts) != 3:
return False
try:
u, v, w = [int(p) for p in parts]
except Exception:
return False
val = (10 * u**3 + 36 * v**3 + 3 * w**3
+ 45 * u**2 * v + 69 * u * v**2
+ 18 * u**2 * w + 12 * u * w**2
+ 42 * v**2 * w + 18 * v * w**2
+ 54 * u * v * w)
return val == 33
def mystery(x):
if type(x) is not int:
return False
n = x
if n <= 0 or n.bit_length() != 62:
return False
if n & 1 == 0:
return False
if n % 10**6 != 413051:
return False
if sum(map(int, str(n))) != 64:
return False
def passes(a):
d = n - 1
s = 0
while d % 2 == 0:
s += 1
d //= 2
y = pow(a, d, n)
if y == 1 or y == n - 1:
return True
for _ in range(s - 1):
y = (y * y) % n
if y == n - 1:
return True
return False
small = (2, 3, 5, 7, 11, 13, 17, 19, 23)
wider = small + (29, 31, 37)
return all(passes(a) for a in small) and not all(passes(a) for a in wider)
def mystery(x):
if type(x) is not tuple or len(x) != 3:
return False
u, v, w = x
if type(u) is not int or type(v) is not int or type(w) is not int:
return False
# Prevent trivial brute-force of small integers
if max(abs(u), abs(v), abs(w)) < 200:
return False
M = [
[u + v + w, 3*u + 9*v + 18*w, 3*u + 6*v + 9*w],
[u + 2*v + 3*w, u + v + w, 3*u + 9*v + 18*w],
[u + 3*v + 6*w, u + 2*v + 3*w, u + v + w]
]
# Calculate the determinant of the 3x3 matrix M
det = (M[0][0] * (M[1][1] * M[2][2] - M[1][2] * M[2][1]) -
M[0][1] * (M[1][0] * M[2][2] - M[1][2] * M[2][0]) +
M[0][2] * (M[1][0] * M[2][1] - M[1][1] * M[2][0]))
return det == 1
def mystery(x):
if type(x) is not str:
return False
if len(x) != 9:
return False
if any(ord(c) > 127 for c in x):
return False
import codecs
import hashlib
y = codecs.decode(x[::-1], "rot_13").encode("latin1")
return hashlib.pbkdf2_hmac(
"sha1",
y,
b"sa\x00lt",
4096,
16,
) == bytes.fromhex("56fa6aa75548099dcc37d7f03425e0c3")
def mystery(x):
if type(x) is not tuple or len(x) != 4:
return False
u, v, w, t = x
if type(u) is not int or type(v) is not int or type(w) is not int or type(t) is not int:
return False
# Prevent Z3 and brute-force tools from guessing small integers
if max(abs(u), abs(v), abs(w), abs(t)) < 100000:
return False
# Linear transformation using a Pascal matrix
a = u + v + w + t
b = u + 2*v + 3*w + 4*t
c = u + 3*v + 6*w + 10*t
d = u + 4*v + 10*w + 20*t
# All variables must be strictly positive and distinct
if len({a, b, c, d}) != 4:
return False
if min(a, b, c, d) <= 0:
return False
# An interesting algebraic identity
left = (a**2 + b**2 + c**2)**2
right = 2 * (a**2 * b**2 + b**2 * c**2 + c**2 * a**2) + d**4
return left == right
def mystery(x):
if type(x) is not int:
return False
n = (
(1 << 1952)
+ (2 << 1856)
+ (3 << 1760)
+ (4 << 1664)
+ (5 << 1568)
+ (6 << 1472)
+ (7 << 1376)
+ (6 << 1280)
+ (5 << 1184)
+ (4 << 1088)
+ (3 << 992)
+ (2 << 896)
+ (1 << 800)
+ (1 << 576)
+ (1 << 480)
+ (1 << 384)
+ (1 << 288)
+ (1 << 192)
+ (1 << 96)
+ 1
)
if not (1 < x < n):
return False
if x.bit_length() != 1472:
return False
if x.bit_count() != 673:
return False
if x & ((1 << 96) - 1):
return False
if ((x >> 96) & 1) != 1:
return False
return pow(x, 7, n) == 1
def mystery(state):
if type(state) is not tuple or len(state) != 3:
return False
x, y, z = state
if type(x) is not int or type(y) is not int or type(z) is not int:
return False
if max(abs(x), abs(y), abs(z)) < 10**7:
return False
left = 6*x**2 + 2*y**2 + 3*z**2 + 6*x*y - 4*x*z
right = (6*x**3 + 3*z**3 + 9*x**2*y - 3*x**2*z
+ 3*x*y**2 - 6*x*z**2 - 3*y**2*z - 9*x*y*z)
return left == right