import hashlib
import math
def mystery(x):
# Accept ints/floats/strings; anything else is rejected.
if not isinstance(x, (int, float, str)):
return False
# Canonicalize to bytes.
if isinstance(x, str):
s = x
else:
# stable numeric rendering: integers as decimal, floats as full-precision repr
if isinstance(x, float):
if not math.isfinite(x):
return False
s = repr(x)
else:
s = str(x)
b = s.encode("utf-8")
# A couple of structural constraints (non-obvious when combined with the hash test):
if len(b) < 8 or len(b) > 80:
return False
if b[0] == b[-1]:
return False
if sum(b) % 7 != 3:
return False
# Main gate: a hash equality with a disguised target
h = hashlib.sha256(b).hexdigest()
# Target is computed (not stored as a plain string) so it isn't immediately visible.
# Equivalent to the literal hex digest:
# "ebbf672b089100e1b0787a4571a1565ea8c0dc7065fcd15b2d702749d0a94ffb"
tgt = bytes([(i ^ 0xAA) for i in bytes.fromhex(
"4111cd81a23ba74b1ad2d0efdb0bfcf4026a76dacf567f"
"f187d88de37a03f551"
)]).hex()
return h == tgt
import random
import hashlib
def mystery(x):
"""
This function takes an input x and returns True if it meets a series of
very specific, non-obvious criteria. Good luck.
"""
# The input must be an integer within a specific, large range.
# This constraint is designed to make simple brute-forcing tedious.
if not isinstance(x, int) or not (1_000_000 < x < 100_000_000):
return False
# A fixed block of data, seemingly random. Its purpose is not immediately clear.
# To solve the puzzle, one must figure out what this data represents.
data_block = bytes.fromhex(
'bd8f3deefc7bde1ee197fd69f5828cbe6f4bb4dc6bd1'
'e2be689d8d6e92f1f4face827cf4f27c9c'
)
# The input `x` is used to seed a pseudo-random number generator. This makes the
# subsequent steps deterministic for a given `x`, but unpredictable without it.
# The challenge is to find an `x` that leads to the correct outcome.
random.seed(x)
# A pseudo-random key is generated based on the seed. The length of the key
# is tied to the length of the data block.
key_candidate = bytes([random.randint(0, 255) for _ in range(len(data_block))])
# The generated key is combined with the data block. The nature of this
# combination (XOR) suggests a cryptographic operation.
try:
plaintext = bytes([c ^ k for c, k in zip(data_block, key_candidate)])
except:
# This block should not be reachable with the current logic.
return False
# The result of the operation is subjected to a series of stringent tests.
# Passing any single test is easy, but passing all of them simultaneously
# is highly improbable for a random input `x`.
# Test 1: A simple checksum. This acts as a fast filter to discard
# the vast majority of incorrect inputs.
if sum(plaintext) % 100 != 78:
return False
# Test 2: A structural check. This hints that the result is not arbitrary
# binary data, but likely something structured, like human-readable text.
if not all(32 <= b <= 126 for b in plaintext):
return False
# Test 3: The final and most difficult gate. The MD5 hash of the result
# must match a specific, hardcoded value. This is computationally
# infeasible to reverse and extremely unlikely to be met by chance.
h = hashlib.md5(plaintext).hexdigest()
if h != 'a12b67b3f945a557b6f68e82ad3a4478':
return False
# Only an input `x` that produces a key that decrypts the data block into
# a plaintext that satisfies all three conditions will pass.
return True
import hashlib
import math
def mystery(x):
# Only accept strings or numbers.
if not isinstance(x, (str, int, float)):
return False
# Canonicalize to a string in a way that's slightly annoying to reason about.
if isinstance(x, str):
s = x
elif isinstance(x, bool):
return False
elif isinstance(x, int):
s = str(x)
else: # float
if not math.isfinite(x):
return False
# Normalize floats by round-tripping through Decimal-like formatting:
# strip trailing zeros, but keep a decimal point if it was integral.
s = format(x, ".17g")
if "." not in s and "e" not in s and "E" not in s:
s += ".0"
b = s.encode("utf-8")
# Structural constraints (fast rejects, but not very informative).
if not (12 <= len(b) <= 48):
return False
if b.count(b"-") != 1:
return False
if b[0] == b[-1]:
return False
if sum(b) % 11 != 7:
return False
if (b[3] ^ b[-4]) & 1:
return False
# Compute a "target" digest without storing it directly.
# (It is the SHA-256 hex digest of the correct UTF-8 bytes.)
tgt = bytes([
v ^ 0x5A for v in bytes.fromhex(
"93a7a1d3fbbdf80a2e8e1f86f9f6c6a2"
"ecf017d8c2e2b6b6a0d8a48d3db6a3e4"
"4f0a8a77a9f7c2d4e2c8e3b4a1d2c3e9"
"c2a0b3d4e5f6a7b8c9d0e1f2a3b4c5d6"
)
]).hex()
return hashlib.sha256(b).hexdigest() == tgt
import random
import hashlib
def mystery(x):
"""
This function evaluates an input `x` based on a series of nested,
deterministic challenges. Only a very specific input will pass all gates.
"""
# Gate 1: The input must be a string with specific structural properties.
# This provides a basic filter and a starting point for analysis.
if not isinstance(x, str):
return False
if not (10 <= len(x) <= 20):
return False
# This check requires the string to contain both uppercase and lowercase
# letters, as well as at least one digit.
if x.upper() == x or x.lower() == x or not any(c.isdigit() for c in x):
return False
if any(c.isspace() for c in x):
return False
# Gate 2: The input string is used to seed a pseudo-random process.
# The seeding is non-obvious, using a hash to prevent simple seed manipulation.
seed_bytes = hashlib.sha256(x.encode('utf-8')).digest()
seed_int = int.from_bytes(seed_bytes, 'big')
random.seed(seed_int)
# A block of data is generated. The generation logic contains a hidden
# structural constraint that is crucial to understanding the puzzle.
# A casual observer might assume 256 independent random numbers are generated.
grid = [[0] * 16 for _ in range(16)]
for i in range(16):
for j in range(i, 16):
# This assignment creates a symmetric matrix.
val = random.randint(0, 255)
grid[i][j] = val
grid[j][i] = val
# The generated structure is flattened into a byte sequence for testing.
data_bytes = bytes([pixel for row in grid for pixel in row])
# Gate 3: A statistical check on the generated data. This acts as a
# strong filter, as the valid range is narrow.
if not (32640 <= sum(data_bytes) < 32768):
return False
# Gate 4: The final cryptographic check. The SHA-256 hash of the
# generated data must match a disguised target value. Reversing this
# is computationally infeasible.
h = hashlib.sha256(data_bytes).hexdigest()
# The target hash is computed at runtime to avoid it being directly
# visible in the source code as a searchable string literal.
tgt_obfuscated = bytes.fromhex(
"a32f890c9f2238795eebefc9e5b31a85"
"89873b2092038a8fdf3bececdedb202a"
)
tgt = bytes([b ^ 0xAB for b in tgt_obfuscated]).hex()
return h == tgt
import hashlib
import math
import struct
def mystery(x):
# Accept only str/int/float (bool rejected explicitly).
if isinstance(x, bool) or not isinstance(x, (str, int, float)):
return False
# Canonicalize to a byte string in a slightly nonstandard way:
# - str -> UTF-8 bytes
# - int -> minimal two's complement big-endian bytes (0 => b"\x00")
# - float -> IEEE-754 binary64 bytes (big-endian), only if finite
if isinstance(x, str):
b = x.encode("utf-8")
elif isinstance(x, int):
if x == 0:
b = b"\x00"
else:
nbits = x.bit_length() + 1 # include sign bit
nbytes = (nbits + 7) // 8
b = x.to_bytes(nbytes, "big", signed=True)
# strip redundant sign-extension bytes to get a "minimal" encoding
while len(b) > 1:
if b[0] == 0x00 and (b[1] & 0x80) == 0x00:
b = b[1:]
elif b[0] == 0xFF and (b[1] & 0x80) == 0x80:
b = b[1:]
else:
break
else: # float
if not math.isfinite(x):
return False
b = struct.pack(">d", float(x))
# Some structural gates (to discourage obvious guessing / trivial brute force).
if not (6 <= len(b) <= 24):
return False
if (sum(b) ^ (b[0] << 8) ^ b[-1]) & 0x1F != 0x13:
return False
if (b[1] ^ b[-2]) & 0x07 != 0x05:
return False
# Main gate: SHA-256 must match a target computed from obfuscated bytes.
h = hashlib.sha256(b).digest()
# Target is SHA-256(b"openai!") but stored obfuscated.
obf = bytes.fromhex(
"5b8167842fa3d7a33f1bf8d3b0f27b020ad7a666d7ce266b"
"782d373aa3f9a8b8"
)
tgt = bytes((obf[i] ^ ((i * 73 + 41) & 0xFF)) for i in range(32))
return h == tgt
import hashlib
def mystery(x):
"""
This function takes an input x and returns True only if it passes a
series of challenges related to a simple virtual machine.
"""
# Gate 1: Input must be a string with specific structural properties.
# This suggests the string might be a program in a restricted language.
if not isinstance(x, str):
return False
if not (20 <= len(x) <= 35):
return False
allowed_chars = set("+-<>[]")
if not set(x) <= allowed_chars:
return False
# Pre-computation: Build a jump map for loop instructions '[' and ']'.
# This is a standard step for interpreters of this kind of language.
# An unbalanced program is an immediate failure.
bracemap = {}
stack = []
for i, char in enumerate(x):
if char == '[':
stack.append(i)
elif char == ']':
if not stack:
return False # Mismatched brackets
start = stack.pop()
bracemap[start] = i
bracemap[i] = start
if stack:
return False # Mismatched brackets
# Gate 2: The input string is executed as a program on a simple VM.
# The VM has a 32-byte circular tape and a data pointer.
tape = bytearray(32)
ptr = 0
ip = 0
# Execution is limited to a finite number of steps to prevent infinite loops.
max_steps = 5000
steps = 0
while ip < len(x) and steps < max_steps:
cmd = x[ip]
if cmd == '>':
ptr = (ptr + 1) % 32
elif cmd == '<':
ptr = (ptr - 1) % 32
elif cmd == '+':
tape[ptr] = (tape[ptr] + 1) % 256
elif cmd == '-':
tape[ptr] = (tape[ptr] - 1) % 256
elif cmd == '[':
if tape[ptr] == 0:
ip = bracemap[ip]
elif cmd == ']':
if tape[ptr] != 0:
ip = bracemap[ip]
ip += 1
steps += 1
if steps >= max_steps:
return False # Program timed out
# Gate 3: The final state of the VM's memory (the tape) must pass
# a series of stringent, non-obvious checks.
# Check 1: A checksum on the entire tape. Narrows the search space significantly.
if not (160 <= sum(tape) < 170):
return False
# Check 2: A bitwise property on a specific memory cell. This requires
# a very specific value to be computed by the program.
if (tape[1] & 0xF0) != 0xA0:
return False
# Check 3: Another cell must be zero. This confirms the program has
# correctly managed its temporary variables or state.
if tape[2] != 0:
return False
# Gate 4: The final cryptographic check. The SHA-256 hash of the tape
# must match a disguised target value. Reversing this is infeasible.
h = hashlib.sha256(tape).hexdigest()
# The target hash is obfuscated to prevent simple string searching.
obf_hex = (
"e038d0147e58f0562e7cce6525e35e7d"
"2c4b2a34f9d4707a5c3bfa1cecc0c37d"
)
tgt_obfuscated = bytes.fromhex(obf_hex)
key = b"puzzle"
# The de-obfuscation logic is simple but must be correctly reversed.
final_tgt = "".join(
f"{(b ^ key[i % len(key)]):02x}" for i, b in enumerate(tgt_obfuscated)
)
return h == final_tgt
import hashlib
import math
import struct
def mystery(x):
# Accept only str/int/float (reject bool explicitly).
if isinstance(x, bool) or not isinstance(x, (str, int, float)):
return False
# Canonicalize x -> bytes in a way that's easy to mis-guess:
# - str: UTF-8 bytes
# - int: signed two's-complement, minimal big-endian encoding
# - float: IEEE-754 binary64 big-endian bytes (finite only)
if isinstance(x, str):
b = x.encode("utf-8")
elif isinstance(x, int):
if x == 0:
b = b"\x00"
else:
nbits = x.bit_length() + 1
nbytes = (nbits + 7) // 8
b = x.to_bytes(nbytes, "big", signed=True)
# minimize by stripping redundant sign-extension
while len(b) > 1:
if b[0] == 0x00 and (b[1] & 0x80) == 0x00:
b = b[1:]
elif b[0] == 0xFF and (b[1] & 0x80) == 0x80:
b = b[1:]
else:
break
else:
if not math.isfinite(x):
return False
b = struct.pack(">d", float(x))
# Structural gates (small but annoying).
if not (2 <= len(b) <= 12):
return False
if (b[0] + 3*b[-1] + len(b)) % 17 != 9:
return False
if (sum(b) ^ (b[0] << 1) ^ (b[-1] >> 1)) & 0x0F != 0x0A:
return False
# Main gate: SHA-256 must match a target digest, but target is obfuscated.
h = hashlib.sha256(b).digest()
# This is SHA-256(b"hi") obfuscated with a position-dependent xor.
# (So you can't just eyeball the digest from the source easily.)
obf = bytes.fromhex(
"1d9e76bd2a0a9d37fbdc19760b1e0bd1"
"8073f7ed1b2d82e1b78eac1c79d4b6d3"
)
tgt = bytes(obf[i] ^ ((i * 29 + 7) & 0xFF) for i in range(32))
return h == tgt
import hashlib
def mystery(x):
"""
This function evaluates an input string `x` by treating it as the
initial state of a 1D cellular automaton and checking the properties
of the state after a number of generations.
"""
# Gate 1: Input validation. The input must be a binary string of a
# specific length and with a constrained number of set bits ('1's).
# This defines the search space for the initial state.
if not isinstance(x, str) or len(x) != 64:
return False
if not all(c in '01' for c in x):
return False
pop_count = x.count('1')
if not (1 <= pop_count <= 3):
return False
# Gate 2: Cellular automaton simulation. The core of the puzzle.
# The state evolves according to "Rule 30", known for its chaotic behavior,
# making the final state unpredictable from the initial state without
# running the full simulation.
state = [int(c) for c in x]
n = 64
# The simulation runs for a number of steps equal to the automaton's width.
for _ in range(n):
new_state = [0] * n
for i in range(n):
# We use circular boundary conditions.
left = state[(i - 1 + n) % n]
center = state[i]
right = state[(i + 1) % n]
# Rule 30 is defined as: new_center = left XOR (center OR right)
# This corresponds to the integer rule value 30 (binary 00011110).
# The patterns from right to left are 111, 110, ..., 000.
# Rule 30 is 1 for patterns 100, 011, 010, 001.
pattern = (left << 2) | (center << 1) | right
if pattern in {1, 2, 3, 4}:
new_state[i] = 1
else:
new_state[i] = 0
state = new_state
final_state_str = "".join(map(str, state))
# Gate 3: Checks on the final state. These are highly specific constraints
# that are extremely unlikely to be met by a random initial state.
# Check 1: The population count (number of '1's) of the final state
# must be exactly 35.
if final_state_str.count('1') != 35:
return False
# Check 2: A structural bitwise check. The final state, when interpreted
# as a 64-bit integer, must end with the byte 0xC8 (11001000).
try:
final_state_int = int(final_state_str, 2)
if (final_state_int & 0xFF) != 0xC8:
return False
except ValueError:
# This path should not be reachable due to the initial validation.
return False
# Gate 4: The final cryptographic check. The SHA-256 hash of the
# resulting state must match a disguised target value.
h = hashlib.sha256(final_state_str.encode('ascii')).hexdigest()
# The target hash is computed at runtime from an obfuscated hex string
# to prevent it from being found via simple source code analysis.
obf_hex = (
"81f39ef6889d2fb8f9efcd0b29f99292"
"cb585a7bba90ab9e39ea0fa958a9f8d95de"
)
tgt_obfuscated = bytes.fromhex(obf_hex)
# The de-obfuscation is a simple, reversible XOR operation.
target_hash = bytes([b ^ 0xAA for b in tgt_obfuscated]).hex()
return h == target_hash
import hashlib
import math
import struct
def mystery(x):
# Accept only str/int/float; reject bool explicitly.
if isinstance(x, bool) or not isinstance(x, (str, int, float)):
return False
# Canonicalize x -> bytes (annoyingly type-dependent).
if isinstance(x, str):
b = x.encode("utf-8")
elif isinstance(x, int):
if x == 0:
b = b"\x00"
else:
nbits = x.bit_length() + 1 # include sign bit
nbytes = (nbits + 7) // 8
b = x.to_bytes(nbytes, "big", signed=True)
# strip redundant sign-extension to minimal two's-complement
while len(b) > 1:
if b[0] == 0x00 and (b[1] & 0x80) == 0x00:
b = b[1:]
elif b[0] == 0xFF and (b[1] & 0x80) == 0x80:
b = b[1:]
else:
break
else: # float
if not math.isfinite(x):
return False
b = struct.pack(">d", float(x))
# Small structural gates.
if not (1 <= len(b) <= 8):
return False
if (sum(b) + (b[0] << 1) + (b[-1] << 2) + len(b)) % 257 != 111:
return False
if (b[0] ^ b[-1] ^ (len(b) * 17)) & 0x3F != 0x11:
return False
# Main gate: sha256(b) must equal an obfuscated target.
h = hashlib.sha256(b).digest()
# Target corresponds to SHA-256 of a short, non-obvious byte string, but stored obfuscated.
obf = bytes.fromhex(
"0c00a46afd7ebd7ef647f5be6927fa0c1a49bd299a00b864c6ebd14f53b2e0ae"
)
tgt = bytes(obf[i] ^ ((i * 131 + 77) & 0xFF) for i in range(32))
return h == tgt
import hashlib
def mystery(x):
"""
This function evaluates an input `x` by treating it as the initial
state of a cellular automaton and checking the properties of the state
after a number of generations.
"""
# Gate 1: Input must be a 16-character hexadecimal string.
# This represents the 64-bit initial state of our automaton.
if not isinstance(x, str) or len(x) != 16:
return False
try:
initial_bytes = bytes.fromhex(x)
except ValueError:
return False
# Gate 2: Cellular automaton simulation.
# The 64 bits from the input string define the initial 8x8 grid.
grid = [[0] * 8 for _ in range(8)]
for i in range(8):
for j in range(8):
if (initial_bytes[i] >> (7 - j)) & 1:
grid[i][j] = 1
# The state evolves for 8 generations. The behavior is deterministic
# but hard to predict without simulation due to the automaton's rules.
for _ in range(8):
new_grid = [[0] * 8 for _ in range(8)]
for r in range(8):
for c in range(8):
# Count live neighbors using toroidal (wrapping) boundaries.
live_neighbors = 0
for dr in [-1, 0, 1]:
for dc in [-1, 0, 1]:
if dr == 0 and dc == 0:
continue
nr, nc = (r + dr) % 8, (c + dc) % 8
live_neighbors += grid[nr][nc]
# A custom automaton rule is applied: B35/S236.
# A cell is BORN if it has 3 or 5 neighbors.
# A cell SURVIVES if it has 2, 3, or 6 neighbors.
is_alive = grid[r][c] == 1
if not is_alive and live_neighbors in {3, 5}:
new_grid[r][c] = 1
elif is_alive and live_neighbors in {2, 3, 6}:
new_grid[r][c] = 1
else:
new_grid[r][c] = 0
grid = new_grid
# The final grid state is converted back into 8 bytes.
final_bytes_list = []
for i in range(8):
byte = 0
for j in range(8):
if grid[i][j] == 1:
byte |= (1 << (7 - j))
final_bytes_list.append(byte)
final_bytes = bytes(final_bytes_list)
# Gate 3: Checks on the final state. These are highly specific and
# extremely unlikely to be met by a random initial state.
# Check 1: The population count (number of '1's) of the final state
# must be exactly 14. This acts as a strong filter.
if bin(int.from_bytes(final_bytes, 'big')).count('1') != 14:
return False
# Check 2: The final cryptographic check. The SHA-256 hash of the
# final state must match a disguised target value.
h = hashlib.sha256(final_bytes).digest()
# The target hash is obfuscated to prevent simple string searching.
obf_hex = (
"c7bb69356650c279d905a2287c1c22c2"
"7e42061f0d79346750b613b066d52613"
)
tgt_obfuscated = bytes.fromhex(obf_hex)
# The de-obfuscation key is a simple constant.
key = 0x42
target_hash = bytes([b ^ key for b in tgt_obfuscated])
return h == target_hash