def mystery(x):
if not isinstance(x, str) or len(x) != 8:
return False
# Convert string to ASCII values
vals = [ord(c) for c in x]
# Constraint 1: Checksum
if sum(vals) != 767:
return False
# Constraint 2: High nibble of the first byte
if (vals[0] & 0xF0) != 0x70:
return False
# Constraint 3: Differential chain
# Each character is related to the next by a specific XOR offset
target_diffs = [67, 92, 25, 1, 29, 89, 94]
current_diffs = [vals[i] ^ vals[i+1] for i in range(len(vals) - 1)]
return current_diffs == target_diffs
def mystery(x):
# Accept only a string; other types are a trap.
if not isinstance(x, str):
return False
# Length gate
if len(x) != (0xB): # 11
return False
# ASCII-ish gate (printable, but not necessarily only alnum)
vals = [ord(c) for c in x]
if any(v < 33 or v > 126 for v in vals):
return False
# --- A handful of "orthogonal" constraints ---
# 1) Sum of all bytes
if sum(vals) != (0x200 + 0x170): # 512 + 368 = 880
return False
# 2) XOR-reduction
xr = 0
for v in vals:
xr ^= v
if xr != (0x72): # 114
return False
# 3) Quadratic-weighted sum mod 1000
w = 0
for i, v in enumerate(vals):
w += v * (i + 1) * (i + 1)
if (w % 1000) != int("56", 16): # 86
return False
# 4) Rolling hash mod 2^16 with a positional XOR perturbation
h = 0
for i, v in enumerate(vals):
t = v ^ (i * 31)
h = ((h * 257) + t) & 0xFFFF
if h != (0xFD3D): # 64829
return False
# 5) Another modular hash (different modulus, different base)
h2 = 0
for v in vals:
h2 = (h2 * 131 + v) % 10007
if h2 != 0x515: # 1301
return False
# 6) Bit-rotation checksum (varied rotation per position)
def rol8(b, r):
r &= 7
return ((b << r) | (b >> (8 - r))) & 0xFF
rs = 0
for i, v in enumerate(vals):
rs += rol8(v, (i * 3) % 8)
if (rs % 1024) != 0x192: # 402
return False
# 7) A few cross-byte relations (to kill off "near misses")
if (vals[0] + vals[-1]) != 0xA3: # 163
return False
if ((vals[1] * vals[-2]) & 0xFF) != 0x09: # 9
return False
if (vals[4] ^ vals[5]) != 0x7E: # 126
return False
if (vals[3] + vals[7]) != 0xBA: # 186
return False
if ((vals[2] * vals[8]) % 251) != 0xA0: # 160
return False
if ((vals[6] - vals[0]) % 97) != 0x50: # 80
return False
return True
def mystery(x):
# Validate input format
if not isinstance(x, str) or len(x) != 16:
return False
# Convert string to ASCII integers
vals = [ord(c) for c in x]
# Initial Vector (IV) for the chaining mechanism
state = [51, 85, 119, 153]
# Mixing Matrix
# A 4x4 matrix used for linear transformation
M = [
[2, 3, 1, 1],
[1, 2, 3, 1],
[1, 1, 2, 3],
[3, 1, 1, 2]
]
# The target output sequence that the input must generate
target = [
95, 255, 131, 64, # Block 1 Output
51, 6, 250, 97, # Block 2 Output
159, 239, 0, 32, # Block 3 Output
133, 86, 182, 116 # Block 4 Output
]
generated_output = []
# Process the input in blocks of 4 bytes
for i in range(0, 16, 4):
block = vals[i:i+4]
# Step 1: Chaining (CBC mode)
# XOR the current block with the state (IV or previous block's output)
mixed = [(b ^ s) for b, s in zip(block, state)]
# Step 2: Linear Transformation
# Multiply the mixed vector by Matrix M modulo 256
transformed = [0] * 4
for r in range(4):
acc = 0
for c in range(4):
acc += M[r][c] * mixed[c]
transformed[r] = acc % 256
# Append result and update state
generated_output.extend(transformed)
state = transformed
return generated_output == target
def mystery(x):
# Accept either an int-like input or a decimal/hex string.
if isinstance(x, bool):
return False
if isinstance(x, int):
n = x
elif isinstance(x, str):
s = x.strip().lower()
if not s:
return False
try:
n = int(s, 16) if s.startswith("0x") else int(s, 10)
except ValueError:
return False
else:
return False
# Range + "looks like a 6-digit code"
if not (100_000 <= n <= 999_999):
return False
ds = str(n)
if len(ds) != 6:
return False
if "0" in ds:
return False
if len(set(ds)) != 6:
return False
# Digit constraints
if sum(ord(c) - 48 for c in ds) != (0b11010): # 26
return False
# Bit/byte constraints
if n.bit_count() != (0xE): # 14
return False
hi, lo = divmod(n, 1000)
if (hi ^ lo) != (0x361): # 865
return False
mix = (n ^ (n >> 3) ^ ((n << 1) & 0xFFFFFFFF)) & 0xFFFF
if mix != int("9e67", 16):
return False
b = n.to_bytes(4, "little", signed=False)
if ((b[0] + b[1] + b[2] + b[3]) & 0xFF) != (0xF6): # 246
return False
# Modular constraints
if (n * 3) % 1000 != (200 - 27): # 173
return False
if (n * n) % 10007 != (0x1637): # 5679
return False
# "Residue fingerprint" (compresses several modular conditions into one check)
mods = [
(1 << 7) - 31, # 97
(1 << 6) + 37, # 101
(0x80) - 25, # 103
(0x6F) + 0x04, # 107
(0x7F) - 18, # 109
(0x70) + 1, # 113
(1 << 7) - 1 # 127
]
acc = 0
for p in mods:
acc = (acc * 131 + (n % p)) & 0xFFFF
# Couple it to n to discourage isolating acc alone.
if (acc ^ ((n >> 5) & 0xFFFF)) != int("cd96", 16):
return False
return True
def mystery(x):
# Constraint 0: Format
if not isinstance(x, str) or len(x) != 12:
return False
v = [ord(c) for c in x]
# Constraint 1: Symmetry / Palindrome Sums
# The string is folded in half; pairs sum to specific constants.
# v[0]+v[11], v[1]+v[10], ...
pair_sums = [100, 212, 208, 223, 217, 197]
if any(v[i] + v[11-i] != pair_sums[i] for i in range(6)):
return False
# Constraint 2: Block XOR Checksums
# The string is divided into 3 blocks of 4 bytes.
if (v[0] ^ v[1] ^ v[2] ^ v[3]) != 45:
return False
if (v[4] ^ v[5] ^ v[6] ^ v[7]) != 0:
return False
if (v[8] ^ v[9] ^ v[10] ^ v[11]) != 82:
return False
# Constraint 3: Linear Weighted Sum
# A specific linear combination of all characters.
# Weights are 1, 2, 3, ..., 12
w_sum = sum(val * (i+1) for i, val in enumerate(v))
if w_sum != 7428:
return False
# Constraint 4: Bitwise Logic on the core
# Specific bitwise relationship between the middle two characters.
if (v[5] & v[6]) != 80:
return False
# Constraint 5: Fixed Anchor
# One character is given for free to anchor the solution.
if v[4] != 95: # '_'
return False
return True
def mystery(x):
# Gate 0: type/shape
if not isinstance(x, str) or len(x) != 16:
return False
# Gate 1: printable ASCII only (no spaces)
if any((ord(ch) < 33 or ord(ch) > 126) for ch in x):
return False
def rol8(b, r):
r &= 7
return ((b << r) | (b >> (8 - r))) & 0xFF
def secret_plain_bytes():
# Reconstruct a hidden 16-byte ASCII plaintext via a keystream XOR.
blob = [246, 124, 22, 133, 28, 15, 86, 191, 184, 160, 16, 168, 141, 168, 180, 115]
s = 0x42
ks = []
for _ in range(16):
s = (s * 45 + 11) & 0xFF
ks.append(s)
return bytes((b ^ k) for b, k in zip(blob, ks))
def round_keys():
# Deterministic (but non-obvious) round keys
s = 0xB7
keys = []
for r in range(6):
k = []
for i in range(16):
s = (s * 109 + 57) & 0xFF
k.append(s ^ ((r * 29 + i * 13) & 0xFF))
keys.append(k)
return keys
def enc(block16: bytes) -> bytes:
st = list(block16)
keys = round_keys()
iv = [0x3C, 0xA1, 0x7E, 0x19, 0xD2, 0x04]
for r in range(6):
# AddRoundKey + position/round bias + rotate
rk = keys[r]
for i in range(16):
st[i] ^= rk[i]
st[i] = (st[i] + ((i * 17 + r * 31 + 0x55) & 0xFF)) & 0xFF
st[i] = rol8(st[i], i + r)
# Permute (bijection on 0..15)
p = [((i * 5 + r * 7) & 15) for i in range(16)]
st = [st[p[i]] for i in range(16)]
# Forward-diffusion chain (invertible, but annoying)
st[0] ^= iv[r]
for i in range(1, 16):
st[i] ^= st[i - 1] ^ ((i * 11 + r * 3) & 0xFF)
return bytes(st)
xb = x.encode("latin1")
target = enc(secret_plain_bytes())
# Extra "noise" checks that still bind to the same target
cx = enc(xb)
if cx != target:
return False
if (sum(cx) ^ (cx[0] * 257 + cx[-1])) & 0xFFFF != (sum(target) ^ (target[0] * 257 + target[-1])) & 0xFFFF:
return False
return True
def mystery(x):
# Sanity check
if not isinstance(x, str) or len(x) != 16:
return False
# 1. Generate Keystream using a Linear Congruential Generator (LCG)
# Parameters: a=5, c=1, m=256, seed=42
keystream = []
state = 42
for _ in range(16):
state = (state * 5 + 1) & 0xFF
keystream.append(state)
# 2. Transform the input
# The transformation involves a "Differential Chaining" mechanism
# combined with the keystream XOR.
# y[i] = (x[i] XOR x[i-1]) XOR k[i]
# For i=0, x[-1] is assumed to be 0.
transformed = []
prev_char_val = 0
for i, char in enumerate(x):
val = ord(char)
# Chain step: XOR with previous character value
chained_val = val ^ prev_char_val
# Stream step: XOR with keystream
encrypted_val = chained_val ^ keystream[i]
transformed.append(encrypted_val)
# Update previous character for the next iteration
prev_char_val = val
# 3. Validation
# The transformed sequence must match exactly.
target = [
144, 12, 180, 39, 185, 243, 230, 85,
214, 159, 250, 152, 68, 182, 135, 157
]
return transformed == target
def mystery(x):
# Gate 0: must be a 10-char printable ASCII string (no spaces)
if not isinstance(x, str) or len(x) != 10:
return False
if any((ord(ch) < 33 or ord(ch) > 126) for ch in x):
return False
# --- Target is stored in a masked form and reconstructed ---
masked = 0x997BB291A1E6CF08BC61 # 10 bytes, big-endian
# mask stream (independent of x)
ms = 0x13
mask = []
for _ in range(10):
ms = (ms * 101 + 17) & 0xFF
mask.append(ms)
masked_bytes = masked.to_bytes(10, "big")
target = bytes((mb ^ mk) for mb, mk in zip(masked_bytes, mask))
# --- Candidate transform ---
# keystream via LCG
s = 0x5A
ks = []
for _ in range(10):
s = (s * 73 + 41) & 0xFF
ks.append(s)
xb = x.encode("latin1")
# stage 1: add keystream
u = [((b + ks[i]) & 0xFF) for i, b in enumerate(xb)]
# stage 2: chained xor with position-dependent bias
v = [0] * 10
v[0] = u[0] ^ 0xC3
for i in range(1, 10):
bias = (i * 17 + 0x3D) & 0xFF
v[i] = u[i] ^ ((v[i - 1] + bias) & 0xFF)
# stage 3: fixed permutation
p = [7, 2, 9, 4, 1, 6, 0, 8, 3, 5]
out = bytes(v[p[i]] for i in range(10))
# "noise" checks (redundant but binding)
sx = sum(out) & 0xFF
xr = 0
for b in out:
xr ^= b
h = 0
for b in out:
h = (h * 257 + b) & 0xFFFF
if sx != 25:
return False
if xr != 13:
return False
if h != 62489:
return False
return out == target
def mystery(x):
# 1. Format Check
if not isinstance(x, str) or len(x) != 16:
return False
# 2. Character Range Check (Printable ASCII)
vals = [ord(c) for c in x]
if any(v < 32 or v > 126 for v in vals):
return False
# 3. Substitution Layer
# Apply a reversible affine transformation to each byte.
# f(v) = (v * 13 + 7) ^ 0xAA (mod 256)
vals = [((v * 13 + 7) & 0xFF) ^ 0xAA for v in vals]
# 4. Permutation Layer
# Shuffle the bytes based on a linear congruential mapping of indices.
# The element at index i moves to index (i * 5 + 3) % 16.
permuted = [0] * 16
for i in range(16):
new_pos = (i * 5 + 3) % 16
permuted[new_pos] = vals[i]
vals = permuted
# 5. Diffusion Layer
# Apply a rolling XOR chain (similar to CBC mode encryption).
iv = 0x55
output = []
for v in vals:
iv = v ^ iv
output.append(iv)
# 6. Target Verification
target = [
124, 38, 164, 56, 237, 107, 252, 140,
140, 183, 203, 88, 229, 82, 83, 108
]
return output == target
def mystery(x):
# Gate 0: type/shape
if not isinstance(x, str) or len(x) != 16:
return False
# Gate 1: printable ASCII, no spaces (keeps search space "reasonable-looking")
if any((ord(ch) < 33 or ord(ch) > 126) for ch in x):
return False
def rol8(b, r):
r &= 7
return ((b << r) | (b >> (8 - r))) & 0xFF
def sbox_gen():
# Deterministic 256-byte "random-looking" permutation derived from a xorshift-like stream.
# (Not cryptographically strong; just messy.)
s = 0xC0FFEE12
pool = list(range(256))
out = []
for i in range(256, 0, -1):
# xorshift32-ish
s ^= (s << 13) & 0xFFFFFFFF
s ^= (s >> 17) & 0xFFFFFFFF
s ^= (s << 5) & 0xFFFFFFFF
j = s % i
out.append(pool.pop(j))
return out # permutation of 0..255
SBOX = sbox_gen()
def secret_plain_bytes():
# Reconstruct a hidden 16-byte ASCII plaintext from an obfuscated blob.
# Steps:
# blob[i] = ( ( secret[q[i]] + delta[i] ) XOR ks[i] ) mod 256
blob = [76, 248, 213, 161, 89, 94, 11, 35, 141, 59, 224, 124, 22, 79, 229, 110]
q = [7, 2, 14, 5, 9, 0, 11, 4, 15, 1, 8, 3, 10, 6, 13, 12]
# ks[i] via LCG: s = (s*73 + 41) mod 256, seeded from 0x5A
ks = []
s = 0x5A
for _ in range(16):
s = (s * 73 + 41) & 0xFF
ks.append(s)
# delta[i] = (i*19 + 0x33) mod 256
delta = [((i * 19 + 0x33) & 0xFF) for i in range(16)]
u = [(blob[i] ^ ks[i]) for i in range(16)]
t = [((u[i] - delta[i]) & 0xFF) for i in range(16)]
# invert the permutation relationship t[i] = secret[q[i]]
secret = [0] * 16
for i, qi in enumerate(q):
secret[qi] = t[i]
return bytes(secret)
def enc(block16: bytes) -> bytes:
b = list(block16)
# Round keys derived deterministically (but "busy-looking")
rk = []
st = 0xA5
for r in range(7):
row = []
for i in range(16):
st = (st * 109 + 57 + (r * 29) + (i * 13)) & 0xFF
row.append(st ^ ((r * 0x3D + i * 0x11) & 0xFF))
rk.append(row)
for r in range(7):
# SubBytes + AddRoundKey + rotate-by-position
for i in range(16):
v = b[i] ^ rk[r][i]
v = SBOX[v]
v = rol8(v, (i + 3 * r + (v & 7)) & 7)
b[i] = v
# Permute indices (bijection on 0..15)
p = [((i * 9 + 5 * r) & 15) for i in range(16)]
b = [b[p[i]] for i in range(16)]
# Diffusion chain with position/round-dependent bias
carry = (0x6B ^ (r * 17)) & 0xFF
for i in range(16):
carry = (carry + rol8(b[(i - 1) & 15], (i + r) & 7) + (i * 13 + r * 7)) & 0xFF
b[i] ^= carry
carry ^= rol8(b[i], (r + i) & 7)
return bytes(b)
xb = x.encode("latin1")
target = enc(secret_plain_bytes())
cx = enc(xb)
# "Noise" checks (fully implied by cx == target, but annoying if you try to shortcut)
if (sum(cx) + (cx[0] ^ cx[7]) + (cx[15] * 3)) & 0xFF != (sum(target) + (target[0] ^ target[7]) + (target[15] * 3)) & 0xFF:
return False
xr = 0
for bb in cx:
xr ^= bb
tr = 0
for bb in target:
tr ^= bb
if xr != tr:
return False
return cx == target