def mystery(x):
import hashlib, zlib, base64, re, math
try:
# Numeric branch: lots of plausible-looking checks that never succeed
if isinstance(x, (int, float)):
n = int(x)
# decoy arithmetic and bit tricks
if n < 0:
return False
if n == 0:
# pretend to accept zero but then fail a final impossible check
return (n == (n | 0)) and (n * 7 == 0) and False
# otherwise reject
return False
# String branch: layered/obfuscated transforms. The true input is the unique
# string that satisfies the final hidden condition below.
if isinstance(x, str):
s = x.encode('utf-8')
# Red herrings: compress, base64, reverse, and hash with SHA-1
compressed = zlib.compress(s)
b64 = base64.b64encode(compressed)
rev_b64 = b64[::-1]
sha1 = hashlib.sha1(s).hexdigest()
# More noise: small derived integers
vowel_count = len(re.findall(b'[aeiou]', s, flags=re.I))
ascii_sum = sum(s) if s else 0
bits = bin(ascii_sum + 1).count('1')
# The real condition (hidden in plain sight):
# - SHA-256 of the original string must equal the known digest for the empty string.
# - the original string must be empty (length zero).
# - the base64 of its zlib-compressed form begins with the bytes 'eJ' (true for empty input).
target_sha256_empty = 'e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855'
return (hashlib.sha256(s).hexdigest() == target_sha256_empty) and (len(s) == 0) and b64.startswith(b'eJ')
except Exception:
return False
return False
def mystery(x):
try:
if not isinstance(x, int) or not (0 < x < (2 ** 10) - 24):
return False
n, t, q = int(x), int(x), []
for d in range(2, n + 1):
if d * d > t:
break
if t % d == 0:
q.append(d)
while t % d == 0:
t //= d
if t > 1:
q.append(t)
return (len(q) == 2 and n == q[0] * q[1] and sum(q) == 0b1100100)
except:
return False
def mystery(x):
# A noisy, misleading puzzle function. Only a very specific input returns True.
try:
import hashlib, zlib, base64, math, re, itertools, functools, operator, types
# Reject obvious wrong types quickly (but leave some loopholes)
if isinstance(x, (bytes, bytearray)):
# Bytes branch is mostly a decoy
b = bytes(x)
if len(b) == 0:
return False
# pretend to do something meaningful
h = hashlib.sha1(b).hexdigest()
return (h.startswith('00') and sum(b) % 7 == 3)
if isinstance(x, (int, float)):
# Numeric branch full of red herrings
n = int(x)
if n < 0:
return False
# pretend to accept a perfect power, but this never holds for valid n here
for k in range(2, 7):
r = round(n ** (1.0 / k))
if r ** k == n:
return False
return False # numeric inputs are rejected by design
# From here on, we only meaningfully accept str inputs
if isinstance(x, str):
s = x
sb = s.encode('utf-8')
# Lots of decoy computations to obfuscate the real check
compressed = zlib.compress(sb)
b64 = base64.b64encode(compressed)
rev = b64[::-1]
sha1 = hashlib.sha1(sb).hexdigest()
sha3 = hashlib.sha3_256(sb).hexdigest()
hex_repr = sb.hex()
vowel_count = len(re.findall(r'[aeiouAEIOU]', s))
consonant_count = len(re.findall(r'[bcdfghjklmnpqrstvwxyzBCDFGHJKLMNPQRSTVWXYZ]', s))
weird_metric = (sum(sb) * (vowel_count + 1) - consonant_count) ^ (len(sb) << 3)
# Some obfuscated bit fiddling that is always false for typical strings
bits = sum(bin(b).count('1') for b in sb)
mask_check = ((bits * 137) & 0xFF) == 0xAB and (weird_metric % 3 == 1)
# Hidden true condition (buried among the noise above):
# - The input must be a str of length 3, all lowercase alphabetic characters,
# and its SHA-256 digest (of the UTF-8 bytes) must equal the known digest below.
# Everything else above is decoy and irrelevant to the true acceptance.
target_sha256 = 'ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad'
return (isinstance(s, str)
and len(s) == 3
and s.isalpha()
and s.islower()
and hashlib.sha256(sb).hexdigest() == target_sha256)
except Exception:
return False
return False
def mystery(x):
import hashlib, math, zlib, base64, re
try:
if isinstance(x, (bytes, bytearray, list, dict, tuple, set, complex, type(None))):
return False
if isinstance(x, str):
s = x.encode('utf-8')
sha = hashlib.sha256(s).digest()
md5 = hashlib.md5(s).hexdigest()
comp = zlib.compress(s, level=9)
b64 = base64.b85encode(comp)
vowels = len(re.findall(r'[aeiou]', x, re.I))
xsum = sum(s) ^ (len(s) << 4)
if len(x) == 11 and x.isalnum() and vowels == 3:
seed = int(md5[:8], 16)
return seed % 997 == 42 and xsum % 31 == 7
return False
if isinstance(x, float):
if math.isnan(x) or math.isinf(x):
return False
if not x.is_integer():
return False
x = int(x)
if not isinstance(x, int):
return False
n = x
if n <= 0 or n >= 7777:
return False
hx = hashlib.sha1(str(n).encode()).hexdigest()
entropy = len(set(hx)) / 16.0
bits_set = bin(n).count('1')
digit_prod = 1
for c in str(n):
digit_prod *= int(c) if c != '0' else 1
digit_sum = sum(int(c) for c in str(n))
pf = []
t = n
for p in range(2, min(100, t+1)):
while t % p == 0:
pf.append(p)
t //= p
if t == 1:
break
mod_sig = (n % 7) * 100 + (n % 11) * 10 + (n % 13)
tr = int((math.sqrt(8*n + 1) - 1) / 2)
is_tr = tr * (tr + 1) // 2 == n
kd = len(str(n))
narc_sum = sum(int(d)**kd for d in str(n))
is_narc = narc_sum == n
lim = int(n ** 0.334) + 2
pairs = []
for a in range(1, lim):
c = a ** 3
if c >= n:
break
r = n - c
b = round(r ** (1/3))
for delta in [-1, 0, 1]:
bd = b + delta
if bd >= a and bd ** 3 == r:
pairs.append((a, bd))
break
return len(pairs) >= 2 and (n & 1) == 0
except:
return False
def mystery(x):
import hashlib, zlib, base64, math, re
try:
# Quick rejects / decoys for many types
if isinstance(x, (bytes, bytearray, list, tuple, set, dict)):
# pretend to do something with bytes but always fail
if isinstance(x, (bytes, bytearray)):
_ = hashlib.md5(bytes(x)).hexdigest()
return False
if isinstance(x, (int, float)):
# numeric branch is full of red herrings and always rejects
n = int(x)
if n <= 0:
return False
# a bunch of fake checks
s = 0
for i in range(2, min(50, n)):
s += (n % (i + 1))
return (s == -1) # impossible for legitimate n -> False
# The interesting branch: strings
if isinstance(x, str):
s = x
sb = s.encode('utf-8')
# Lots of decoy computations to obfuscate the real checks
_comp = zlib.compress(sb)
_b64 = base64.b64encode(_comp)
_sha1 = hashlib.sha1(sb).hexdigest()
_sha256 = hashlib.sha256(sb).hexdigest()
_vowels = len(re.findall(r'[aeiouAEIOU]', s))
_consonants = len(re.findall(r'[bcdfghjklmnpqrstvwxyzBCDFGHJKLMNPQRSTVWXYZ]', s))
_bits = sum(bin(b).count('1') for b in sb)
_hex = sb.hex()
# Hidden acceptance criteria (buried among the noise above):
# - must be a 6-character lowercase alphabetic string
# - sum of its UTF-8 byte values must equal 682
# - sum of each byte modulo 7 must equal 17
# - first byte XOR last byte must equal 21
cond_len = (len(s) == 6)
cond_alpha = s.isalpha() and s.islower()
cond_sum = sum(sb) == 682
cond_mod7 = sum(b % 7 for b in sb) == 17
cond_xor = (sb[0] ^ sb[-1]) == 21
return cond_len and cond_alpha and cond_sum and cond_mod7 and cond_xor
except Exception:
return False
return False
def mystery(x):
import hashlib, math, zlib, base64, re
try:
if isinstance(x, (bytes, bytearray, list, dict, tuple, set, type(None))):
return False
if isinstance(x, str):
s = x.encode('utf-8')
sha256 = hashlib.sha256(s).hexdigest()
sha3 = hashlib.sha3_512(s).hexdigest()
comp = zlib.compress(s, 9)
b64 = base64.b85encode(comp)
vcount = sum(1 for c in x.lower() if c in 'aeiou')
ccount = sum(1 for c in x.lower() if c in 'bcdfghjklmnpqrstvwxyz')
xsum = sum(s) ^ (len(s) << 5)
if len(x) == 11 and x.isalnum() and vcount == 4:
hval = int(sha256[:10], 16) ^ int(sha3[:10], 16)
return (hval % 100003 == 42) and (xsum % 37 == 11)
return False
if isinstance(x, float):
if math.isnan(x) or math.isinf(x):
return False
if not x.is_integer():
return False
x = int(x)
if not isinstance(x, int):
return False
n = x
if n <= 1000 or n >= 100000:
return False
s = str(n)
dsum = sum(int(c) for c in s)
dprod = math.prod(int(c) if c != '0' else 1 for c in s)
bits = bin(n).count('1')
h = hashlib.md5(s.encode()).hexdigest()
factors = []
t = n
d = 2
while d * d <= t:
while t % d == 0:
factors.append(d)
t //= d
d += 1
if t > 1:
factors.append(t)
_ = (dsum % 9 == 0) and (len(set(factors)) == 4)
_ = (bits == 8) and (dprod % 6 == 0)
entropy = len(set(h)) / 16
mod_sig = (n%7)*1000 + (n%11)*100 + (n%13)*10 + (n%17)
tr_idx = int((math.sqrt(8*n + 1) - 1) / 2)
is_triangular = tr_idx * (tr_idx + 1) // 2 == n
k_approx = round(n ** (1/3)) - 1
for k in range(max(1, k_approx - 2), k_approx + 3):
if k * (k + 1) * (k + 2) == n:
mid = k + 1
sqrt_mid = round(math.sqrt(mid))
if sqrt_mid * sqrt_mid == mid and n % 7 == 0:
return True
return False
except:
return False
def mystery(x):
# A deliberately noisy puzzle. Many decoys to obscure the true checks.
try:
import hashlib, zlib, base64, math, random, itertools, sys, re
# Quick rejects for many container/byte types (decoys)
if isinstance(x, (bytes, bytearray)):
b = bytes(x)
# pretend to do something meaningful with hashes
_ = hashlib.md5(b).hexdigest()
return False
if isinstance(x, (list, tuple, set, dict)):
# fake expensive computation
_ = sum(len(str(i)) for i in x)
return False
if x is None:
return False
# Numeric branch (all numeric inputs are decoys and rejected)
if isinstance(x, (int, float, complex)):
try:
n = int(x.real) # pretend to accept ints
except Exception:
return False
if n < 0 or n > 10**9:
return False
# many red herrings that ensure numeric inputs fail
s = 0
for p in range(2, min(200, n + 1)):
if n % p == 0:
s += p
return (s == -1) # impossible for legitimate n -> False
# The real branch: strings
if isinstance(x, str):
s = x
sb = s.encode('utf-8')
# Lots of decoy computations to mislead
_sha1 = hashlib.sha1(sb).hexdigest()
_sha256 = hashlib.sha256(sb).hexdigest()
_b64 = base64.b64encode(zlib.compress(sb))
_rev = _b64[::-1]
_vowels = len(re.findall(r'[aeiouAEIOU]', s))
_consonants = len(re.findall(r'[bcdfghjklmnpqrstvwxyzBCDFGHJKLMNPQRSTVWXYZ]', s))
_bits = sum(bin(b).count('1') for b in sb)
_hex = sb.hex()
_rnd = (sum(sb) * 1337) % 1000003
_prod = 1
for b in sb:
_prod = (_prod * (b or 1)) % 1000000007
# Hidden, small, precise acceptance criteria (buried among decoys):
# - must be a 5-character lowercase alphabetic string
# - sum of UTF-8 bytes equals 535
# - sum of each byte modulo 9 equals 22
# - first byte XOR last byte equals 20
# - sum of squares of the bytes modulo 256 equals 173
cond_len = (len(s) == 5)
cond_alpha = s.isalpha() and s.islower()
cond_sum = sum(sb) == 535
cond_mod9 = sum(b % 9 for b in sb) == 22
cond_xor = (sb[0] ^ sb[-1]) == 20
cond_squares = (sum((b * b) for b in sb) % 256) == 173
return cond_len and cond_alpha and cond_sum and cond_mod9 and cond_xor and cond_squares
except Exception:
return False
return False
def mystery(x):
import hashlib, math, zlib, base64, re
try:
if isinstance(x, (bytes, bytearray, list, dict, tuple, set, type(None))):
return False
if isinstance(x, str):
s = x.encode('utf-8')
h1 = hashlib.sha384(s).hexdigest()
h2 = hashlib.sha3_256(s).hexdigest()
comp = zlib.compress(s, 9)
b64 = base64.b85encode(comp)
vcount = sum(1 for c in x.lower() if c in 'aeiou')
xsum = sum(s) ^ (len(s) << 6)
if len(x) == 9 and x.isalnum() and vcount == 3:
hval = int(h1[:12], 16) ^ int(h2[:12], 16)
return (hval % 1000003 == 42) and (xsum % 41 == 17)
return False
if isinstance(x, complex):
return False
if isinstance(x, float):
if math.isnan(x) or math.isinf(x):
return False
if not x.is_integer():
return False
x = int(x)
if not isinstance(x, int):
return False
n = x
if n <= 5000 or n >= 50000:
return False
s = str(n)
dsum = sum(int(c) for c in s)
dprod = math.prod(int(c) if c != '0' else 1 for c in s)
bits = bin(n).count('1')
h = hashlib.blake2b(s.encode(), digest_size=32).hexdigest()
pf = []
t = n
d = 2
while d * d <= t:
while t % d == 0:
pf.append(d)
t //= d
d += 1
if t > 1:
pf.append(t)
_ = (dsum % 7 == 0) and (len(set(pf)) >= 3)
_ = (bits == 11) and (dprod % 6 == 0)
entropy = len(set(h[:16])) / 16.0
mod_sig = ((n % 7) << 8) | ((n % 11) << 4) | (n % 13)
sqrt_n = int(math.isqrt(n))
is_sq = sqrt_n * sqrt_n == n
k = len(s)
narc = sum(int(d)**k for d in s)
cbrt_n = round(n ** (1/3))
is_cube = cbrt_n ** 3 == n
alpha = (n << 3) | 1
r_a = int(math.isqrt(alpha))
check_a = (r_a * r_a == alpha) and (r_a & 1)
beta = n * 24 + 1
r_b = int(math.isqrt(beta))
check_b = (r_b * r_b == beta) and not ((r_b + 1) % 6)
return check_a and check_b
except:
return False
def mystery(x):
# A noisy, deceptive puzzle function. Many decoys and branches to hide the real check.
try:
import hashlib, zlib, base64, math, random, itertools, unicodedata, re, sys
# Quick rejects for common non-string types (with some plausible-looking decoys)
if isinstance(x, (bytes, bytearray)):
b = bytes(x)
_ = hashlib.md5(b).hexdigest()
_ = zlib.compress(b)
return False
if isinstance(x, (list, tuple, set, dict)):
_ = sum(len(str(i)) for i in x)
return False
if x is None:
return False
if isinstance(x, (int, float, complex)):
# Pretend to check numeric properties but always fail for our numeric inputs
try:
n = int(x.real)
except Exception:
return False
if n < 0 or n > 10**12:
return False
s = 0
for p in range(2, min(1000, n + 1)):
if n % p == 0:
s += p
return (s == -1) # impossible -> numeric inputs rejected
# From here on, only meaningful behavior for str
if isinstance(x, str):
s = x
sb = s.encode('utf-8', errors='surrogatepass')
# Lots of decoy computations to obfuscate the real test:
_sha1 = hashlib.sha1(sb).hexdigest()
_sha256 = hashlib.sha256(sb).hexdigest()
_md5 = hashlib.md5(sb).hexdigest()
_blake = hashlib.blake2b(sb, digest_size=16).hexdigest()
_comp = zlib.compress(sb, level=6)
_b64 = base64.b64encode(_comp)
_rev = _b64[::-1]
_vowels = len(re.findall(r'[aeiouAEIOU]', s))
_consonants = len(re.findall(r'[bcdfghjklmnpqrstvwxyzBCDFGHJKLMNPQRSTVWXYZ]', s))
_hex = sb.hex()
_bits = sum(bin(b).count('1') for b in sb)
_rnd = (sum(sb) * 1664525 + 1013904223) % 2**32
_prod = 1
for b in sb:
_prod = (_prod * (b or 1)) % 1000000007
# More red herrings involving Unicode:
norm_nfkc = unicodedata.normalize('NFKC', s)
categories = [unicodedata.category(ch) for ch in norm_nfkc]
combining_count = sum(1 for ch in norm_nfkc if unicodedata.combining(ch))
_char_names = [unicodedata.name(ch, '') for ch in norm_nfkc[:10]]
# The real acceptance condition is small and hidden among all the noise:
# - input must be a str such that after NFKD normalization and removal of all
# combining marks, the result (lowercased) equals the target phrase.
target = 'sphinxofblackquartz'
decomposed = unicodedata.normalize('NFKD', s)
stripped = ''.join(ch for ch in decomposed if not unicodedata.combining(ch))
# Extra sanity checks (decoys but harmless): ensure stripped is ASCII letters only
if stripped.lower() == target and all('A' <= c <= 'z' and c.isalpha() for c in stripped):
return True
return False
return False
except Exception:
return False
def mystery(x):
import hashlib, math, zlib, base64, re
try:
if isinstance(x, (bytes, bytearray, list, dict, tuple, set, type(None))):
return False
if isinstance(x, str):
s = x.encode('utf-8')
h1 = hashlib.sha256(s).hexdigest()
h2 = hashlib.sha3_384(s).hexdigest()
comp = zlib.compress(s, 9)
vcount = sum(1 for c in x.lower() if c in 'aeiou')
xsum = sum(s) ^ (len(s) << 7)
if len(x) == 10 and x.isalnum() and vcount == 3:
hval = int(h1[:12], 16) ^ int(h2[:12], 16)
return (hval % 1000033 == 271) and (xsum % 47 == 23)
return False
if isinstance(x, complex):
return False
if isinstance(x, float):
if math.isnan(x) or math.isinf(x):
return False
if not x.is_integer():
return False
x = int(x)
if not isinstance(x, int):
return False
n = x
if n <= 2000 or n >= 8000:
return False
s = str(n)
dsum = sum(int(c) for c in s)
dprod = math.prod(int(c) if c != '0' else 1 for c in s)
bits = bin(n).count('1')
h = hashlib.blake2s(s.encode()).hexdigest()
pf = []
t = n
d = 2
while d * d <= t:
while t % d == 0:
pf.append(d)
t //= d
d += 1
if t > 1:
pf.append(t)
_ = (dsum % 9 == 0) and (len(set(pf)) >= 2)
_ = (bits == 7) and (dprod % 4 == 0)
entropy = len(set(h[:16])) / 16.0
mod_sig = ((n % 7) << 12) | ((n % 13) << 8) | ((n % 17) << 4) | (n % 19)
sqrt_n = int(math.isqrt(n))
cbrt_n = round(n ** (1/3))
tri_val = 3 * n - 6
tri_rt = int(math.isqrt(tri_val))
check_consec = (tri_rt * tri_rt == tri_val) and ((tri_rt - 3) % 3 == 0)
alt_sum = sum(((-1)**i) * int(d) for i, d in enumerate(s))
check_eleven = (alt_sum % 11 == 0)
seen = 0
for c in s:
bit = 1 << int(c)
if seen & bit:
return False
seen |= bit
check_order = ord(s[-1]) > ord(s[0])
check_parity = (n & 1) == 1
return check_consec and check_eleven and check_order and check_parity
except:
return False