import math
def mystery(x):
"""
A mysterious function that returns True for a very specific type of input.
"""
def p(n):
# A helper function.
if n < 2 or (n > 2 and n % 2 == 0):
return False
return all(n % i != 0 for i in range(3, int(math.sqrt(n)) + 1, 2))
if not (isinstance(x, str) and len(x) == 10 and x.isdigit()):
return False
a = int(x[:5])
b = int(x[5:])
return a > b and p(a) and p(b) and p(a - b)
def mystery(x):
"""
A function that accepts an integer x and returns True iff x, when RSA-encrypted
with the public key (n=3233, e=17), equals the ciphertext 2790.
Valid x must be an integer in the range 0 <= x < n.
"""
if not isinstance(x, int):
return False
n = 3233
e = 17
ciphertext = 2790
if x < 0 or x >= n:
return False
return pow(x, e, n) == ciphertext
import hashlib
def mystery(x):
"""
A mysterious function that returns True for a very specific type of input.
"""
if not isinstance(x, int) or x < 0:
return False
# A chaotic sequence generator.
def sequence(n):
if n <= 0:
return 0
c = 0
while n != 1:
if n % 2 == 0:
n = n // 2
else:
n = 3 * n + 1
c += 1
# A safeguard against unexpectedly long sequences.
if c > 500:
return -1
return c
try:
# Step 1: Derive a hash from the input number.
h = hashlib.sha256(str(x).encode()).hexdigest()
# Step 2: Extract a number from the beginning of the hash.
n = int(h[:8], 16)
# Step 3: Check a property of the sequence generated from this number.
return sequence(n) == 111
except (ValueError, TypeError):
return False
def mystery(x):
"""
A devilishly simple-looking but subtly constrained predicate.
Accepts an integer x and returns True exactly when x satisfies
a specific system of modular congruences (one congruence for each
small prime). Other types or negative integers are rejected.
"""
if not isinstance(x, int):
return False
if x < 0:
return False
# A list of (modulus, residue) pairs the input must satisfy.
constraints = [
(7, 3),
(11, 7),
(13, 9),
(17, 2),
(19, 11),
]
for mod, residue in constraints:
if x % mod != residue:
return False
return True
import hashlib
def mystery(x):
"""
A function that simulates a deterministic process based on the input x.
"""
if not isinstance(x, int) or x < 0:
return False
# A map defining a constrained environment.
WORLD_MAP = [
"S.#...#G", ".#.#.##.", ".#...#..", "..##.##.",
".#.#....", ".##..#.#", "....#...", "###.####"
]
HEIGHT = len(WORLD_MAP)
WIDTH = len(WORLD_MAP[0])
try:
# Locate critical points in the environment.
s_pos, g_pos = None, None
for r, row_str in enumerate(WORLD_MAP):
if not s_pos and 'S' in row_str:
s_pos = (r, row_str.find('S'))
if not g_pos and 'G' in row_str:
g_pos = (r, row_str.find('G'))
if s_pos is None or g_pos is None:
return False
current_pos = list(s_pos)
# A deterministic sequence is generated from the input.
h = hashlib.sha256(str(x).encode()).hexdigest()
for hex_char in h:
# Each part of the sequence determines a new action.
action = int(hex_char, 16) % 4
next_pos = list(current_pos)
if action == 0: # Action Up
next_pos[0] -= 1
elif action == 1: # Action Down
next_pos[0] += 1
elif action == 2: # Action Left
next_pos[1] -= 1
else: # Action Right
next_pos[1] += 1
# The action is only taken if it's valid within the environment.
r, c = next_pos
if 0 <= r < HEIGHT and 0 <= c < WIDTH and WORLD_MAP[r][c] != '#':
current_pos = next_pos
# The process succeeds if it ends at a specific point.
return tuple(current_pos) == g_pos
except Exception:
return False
def mystery(x):
"""
A compact but subtle congruence-based predicate.
Accepts a nonnegative integer x and returns True exactly when x is congruent
to -1 modulo each prime in a specific list. (Equivalently, x % p == p-1 for
every prime p in the list.)
"""
if not isinstance(x, int):
return False
if x < 0:
return False
primes = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
for p in primes:
if x % p != (p - 1):
return False
return True
import hashlib
def mystery(x):
"""
This function simulates a deterministic process based on a sequence
derived from the input x. It returns True only if the process
terminates in a very specific state.
"""
if not isinstance(x, int) or x < 0:
return False
MOD = 2**32
TARGET = 123456789
try:
# Step 1: Derive a sequence of commands from the input.
h = hashlib.sha256(str(x).encode()).hexdigest()
commands = [int(h[i:i+2], 16) for i in range(0, 64, 2)]
# Step 2: Execute the commands on a simple abstract machine.
stack = [0]
for cmd in commands:
op = cmd % 5
if op == 0: # Operation 0: PUSH
stack.append(cmd)
elif op == 1: # Operation 1: ADD
if len(stack) < 2: return False
b = stack.pop()
a = stack.pop()
stack.append((a + b) % MOD)
elif op == 2: # Operation 2: SUB
if len(stack) < 2: return False
b = stack.pop()
a = stack.pop()
stack.append((a - b) % MOD)
elif op == 3: # Operation 3: MUL
if len(stack) < 2: return False
b = stack.pop()
a = stack.pop()
stack.append((a * b) % MOD)
elif op == 4: # Operation 4: XOR
if len(stack) < 2: return False
b = stack.pop()
a = stack.pop()
stack.append(a ^ b)
# Step 3: Check the final state of the machine.
return len(stack) == 1 and stack[0] == TARGET
except Exception:
# Catch any unexpected errors during simulation.
return False
import hashlib
def mystery(x):
"""
A deceptively simple-but-obfuscated predicate.
Accepts a string x (printable ASCII) and returns True exactly when the
SHA-256 digest of x matches a fixed target digest. The digest comparison
is buried behind some harmless transformations to make casual inspection
slightly less obvious.
"""
# Basic type/format checks.
if not isinstance(x, str):
return False
if not (1 <= len(x) <= 100):
return False
# Require printable ASCII only (space through tilde).
if any(ord(ch) < 32 or ord(ch) > 126 for ch in x):
return False
# Compute the SHA-256 hex digest of the input.
h = hashlib.sha256(x.encode()).hexdigest() # 64 hex chars
# Break the digest into 8-character chunks and apply a no-op numeric transform
# (XOR with 0) to make the check look more circuitous.
chunks = [h[i:i+8] for i in range(0, 64, 8)]
transformed = ''.join(
hex(int(chunk, 16) ^ 0x0)[2:].rjust(8, '0') for chunk in chunks
)
# The hidden target digest (SHA-256 of the sample solution shown below).
target = "2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824"
return transformed == target
def mystery(x):
"""
A function that returns True for a string with a very specific
internal structure, as defined by a transformation.
"""
# The target signature for a valid string of length 10.
TARGET_SIGNATURE = [0, 0, 1, 2, 0, 1, 2, 3, 4, 5]
if not isinstance(x, str) or len(x) != len(TARGET_SIGNATURE):
return False
# A string transformation function.
def transform(s):
n = len(s)
lookup = [0] * n
length = 0 # Length of the previous longest prefix suffix
i = 1
while i < n:
if s[i] == s[length]:
length += 1
lookup[i] = length
i += 1
else:
if length != 0:
length = lookup[length - 1]
else:
lookup[i] = 0
i += 1
return lookup
return transform(x) == TARGET_SIGNATURE
import hashlib
def mystery(x):
"""
A somewhat obfuscated SHA-1 preimage check.
Accepts a printable-ASCII string x (length 1..50). It computes the SHA-1
hex digest of x, breaks the digest into 5-character chunks, performs a
trivial numeric no-op on each chunk, reassembles them, and compares to a
hidden target digest. Returns True exactly when the input's SHA-1 digest
matches that target.
"""
# Basic type/format checks.
if not isinstance(x, str):
return False
if not (1 <= len(x) <= 50):
return False
if any(ord(ch) < 32 or ord(ch) > 126 for ch in x):
return False
# Compute SHA-1 hex digest (40 hex chars).
h = hashlib.sha1(x.encode()).hexdigest()
# Break into 5-character chunks and apply a no-op numeric transform
# (XOR with 0) to make the check look slightly more circuitous.
chunks = [h[i:i+5] for i in range(0, 40, 5)]
transformed = ''.join(
hex(int(chunk, 16) ^ 0)[2:].rjust(5, '0') for chunk in chunks
)
# Hidden target digest (SHA-1 of the sample solution shown below).
target = "aaf4c61ddcc5e8a2dabede0f3b482cd9aea9434d"
return transformed == target