def mystery(x):
if not isinstance(x, str):
return False
if len(x) != 8:
return False
if not x.isalnum():
return False
a = sum(ord(c) for c in x)
b = sum(ord(c)**2 for c in x[::-1])
if a % 17 != 5:
return False
if b % 31 != 13:
return False
if x[0] != x[4]:
return False
if x[1:4] != x[5:8][::-1]:
return False
return True
def mystery(x):
if not isinstance(x, int) or not (10**12 <= x < 10**13):
return False
v = [(x // (1000**i)) % 1000 for i in range(3)]
v.append(x // 1000**3)
if (v[3] ^ v[2]) != 234:
return False
if (v[2] & v[1]) != 24:
return False
if (v[1] | v[0]) != 959:
return False
if sum(v) != 2785:
return False
if (v[3] * v[1]) % 1000 != 672:
return False
if (v[2] * v[0]) % 511 != 77:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if not (10**9 <= x < 10**10):
return False
digits = [int(c) for c in str(x)]
if sum(digits) != 47:
return False
if sum(d*d for d in digits) != 261:
return False
if digits[0] * digits[9] != 36:
return False
if digits[3] - digits[5] != 4:
return False
s = 0
for i, d in enumerate(digits):
s = (s * 10 + d) ^ (i * 7 + 3)
if s % 1000003 != 20166:
return False
return True
def mystery(x):
if not isinstance(x, int) or not (0 <= x < 2**64):
return False
a = x & 0xFFFFFFFF
b = x >> 32
# Left-rotate 'a' by 13 bits
a_rot = ((a << 13) | (a >> 19)) & 0xFFFFFFFF
# Bitwise and arithmetic constraints
if a_rot + b != 0xC567C567:
return False
if a_rot ^ b != 0xC167C167:
return False
if bin(x).count('1') != 20:
return False
if (a * b) % 2**32 != 0x5D38E2F4:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if not (10**7 <= x < 10**8):
return False
s = str(x)
digits = [int(c) for c in s]
if sum(digits) != 28:
return False
if sum(d*d for d in digits) != 136:
return False
if digits[0] * digits[2] * digits[4] * digits[6] != 9:
return False
if digits[1] + digits[3] + digits[5] + digits[7] != 20:
return False
h = 0
for i, d in enumerate(digits):
h = (h * 37 + d * (i + 1)) % 1000003
if h != 753442:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if not (10**18 <= x < 10**19):
return False
s = str(x)
digits = [int(d) for d in s]
if sum(digits) != 77:
return False
a = x & 0xFFFFFFFF
b = x >> 32
# Bitwise and arithmetic relationships between the two halves of x
if (a ^ b) != 0x85611301:
return False
if (a + b) != 0xA9699361:
return False
# Modular constraint
if x % 1234567 != 1087003:
return False
# Polynomial rolling hash of the digits
h = 0
for d in digits:
h = (h * 31 + d) % 1000007
return h == 7163
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if not (10**11 <= x < 10**12):
return False
digits = [int(c) for c in str(x)]
if sum(digits) != 60:
return False
if sum(d*d for d in digits) != 400:
return False
if digits[0] + digits[5] != 10:
return False
if digits[2] * digits[7] != 24:
return False
if digits[1] + digits[3] + digits[4] + digits[9] + digits[10] + digits[11] != 21:
return False
h = 0
for i, d in enumerate(digits):
h = (h * 31 + d * (i + 1)) % 999983
if h != 271744:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if not (10**15 <= x < 10**16):
return False
# Digit-based properties
s = str(x)
d = [int(c) for c in s]
if sum(d) != 79 or sum(i**2 for i in d) != 517:
return False
# Bitwise relationships between the halves of x
hi, lo = x >> 32, x & 0xffffffff
if hi + lo != 1860223474 or hi ^ lo != 1859665346:
return False
# Population count
if bin(x).count('1') != 27:
return False
# Modular arithmetic constraints
if x % 1000003 != 234 or x % 1234567 != 467624:
return False
return True
def mystery(x):
if not isinstance(x, str):
return False
if len(x) != 10:
return False
if not all(c.isalnum() for c in x):
return False
codes = [ord(c) for c in x]
if sum(codes) != 755:
return False
if codes[0] ^ codes[9] != 125:
return False
if codes[1] * codes[8] != 5252:
return False
if codes[2] + codes[3] != 216:
return False
h = 0
for i, c in enumerate(codes):
h = (h * 131 + c * (i+1)) % 1000003
if h != 5157:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if not (10**11 <= x < 10**12):
return False
# Digit-based constraints
s = str(x)
digits = [int(d) for d in s]
if sum(digits) != 31 or sum(d**2 for d in digits) != 155:
return False
# Bitwise constraints on a 20-bit split
hi = x >> 20
lo = x & 0xfffff
if hi + lo != 271900 or hi ^ lo != 247324:
return False
# Population count (number of set bits in binary)
if bin(x).count('1') != 13:
return False
# Modular arithmetic constraints
if x % 1234567 != 400508 or x % 1000003 != 584812:
return False
# Product constraint on the split parts
if (hi * lo) % 1000007 != 397848:
return False
return True