def mystery(x):
if not isinstance(x, str): return False
if len(x) != 10: return False
if not x.isdigit(): return False
if len(set(x)) != 10: return False
if x[0] == '0': return False
primes = [2, 3, 5, 7, 11, 13, 17]
for i, p in enumerate(primes):
if int(x[i+1:i+4]) % p:
return False
return True
import codecs
import hashlib
import hmac
def mystery(x):
if type(x) is not str:
return False
if len(x) != 56:
return False
if any(c < "a" or c > "z" for c in x):
return False
y = codecs.decode(x, "rot_13")
return hmac.compare_digest(
hashlib.sha256(y.encode("ascii")).hexdigest(),
"248d6a61d20638b8e5c026930c3e6039a33ce45964ff2167f6ecedd419db06c1",
)
def mystery(x):
if not isinstance(x, str): return False
if len(x) != 12: return False
if not x.isdigit(): return False
if x[0] == '0': return False
n = int(x)
M = 10**12
return (n * n) % M == n
def mystery(x):
if type(x) is not int:
return False
if not (10**14 < x < 10**15):
return False
def ok(n, a):
if n % a == 0:
return n == a
d = n - 1
s = 0
while d % 2 == 0:
s += 1
d //= 2
y = pow(a, d, n)
if y == 1 or y == n - 1:
return True
for _ in range(s - 1):
y = (y * y) % n
if y == n - 1:
return True
return False
if x % 10670053 != 0:
return False
return all(ok(x, a) for a in (2, 3, 5, 7, 11, 13, 17))
def mystery(x):
if type(x) is not int:
return False
if x <= 1 or x >= 10**12:
return False
D = 73
diff = x * x - 1
if diff % D != 0:
return False
y2 = diff // D
y = int(round(y2 ** 0.5))
# adjust for float imprecision
while y > 0 and y * y > y2:
y -= 1
while (y + 1) * (y + 1) <= y2:
y += 1
return y > 0 and y * y == y2
def mystery(x):
if type(x) is not int:
return False
n = int(
"152260502792253336053561837813263742971806811496138068865790849458"
"0122963258952897654000350692006139"
)
if not (10**49 < x < 10**50):
return False
if x % 1000 != 199:
return False
return n % x == 0
def mystery(x):
if type(x) is not str:
return False
if len(x) != 10:
return False
if not all('a' <= c <= 'z' for c in x):
return False
h1 = h2 = 0
P1, B1 = 10**9 + 7, 26
P2, B2 = 10**9 + 9, 27
for c in x:
v = ord(c) - 97
h1 = (h1 * B1 + v) % P1
h2 = (h2 * B2 + v) % P2
return h1 == 746758610 and h2 == 906464440
def mystery(x):
if type(x) is not str:
return False
n = 52
if len(x) != 2 * n:
return False
if any(c < "0" or c > "9" for c in x):
return False
p = [int(x[i:i + 2]) for i in range(0, 2 * n, 2)]
if sorted(p) != list(range(1, n + 1)):
return False
seen = set()
for i, a in enumerate(p):
for j in range(i + 1, n):
d = (j - i, p[j] - a)
if d in seen:
return False
seen.add(d)
return True
def mystery(x):
if type(x) is not str: return False
if len(x) != 81: return False
if not all(c in "123456789" for c in x): return False
given = "800000000003600000070090200050007000000045700000100030001000068008500010090000400"
for i in range(81):
if given[i] != '0' and given[i] != x[i]:
return False
for i in range(9):
if set(x[i*9:(i+1)*9]) != set("123456789"): return False
if set(x[i::9]) != set("123456789"): return False
for br in range(3):
for bc in range(3):
box = [x[(br*3+r)*9 + bc*3+c] for r in range(3) for c in range(3)]
if set(box) != set("123456789"): return False
return True
def mystery(x):
if type(x) is not str:
return False
n = 1019
if len(x) != n:
return False
if x.count("1") != 509 or x.count("0") != 510:
return False
b = [c == "1" for c in x]
for d in range(1, n):
if sum(b[i] and b[(i + d) % n] for i in range(n)) != 254:
return False
return True