def mystery(x):
try:
n = int(x)
if n <= 1:
return False
p, q = 1, 1
while q < n:
p, q = q, p + q
if q != n:
return False
t = 0
for i, c in enumerate(str(n)):
t += int(c) ** (i + 1)
return t % 7 == 0 and t != 0
except:
return False
def mystery(x):
try:
if not isinstance(x, str):
return False
if len(x) != 6:
return False
o = [ord(c) for c in x]
if any(not ((65 <= oi <= 90) or (97 <= oi <= 122)) for oi in o):
return False
if sum(o) % 7 != 3:
return False
s = 0
for i in range(6):
s += o[i] * (i + 1)
if s != 1885:
return False
p = 1
for oi in o:
p = (p * oi) % 10007
if p != 5577:
return False
if x[2].lower() != 'c' or x[0].lower() != x[5].lower():
return False
return True
except:
return False
def mystery(x):
try:
n = int(x)
if n <= 0:
return False
def to_base_k(num, k):
if num == 0: return [0]
d = []
while num > 0:
d.append(num % k)
num //= k
return d
d3 = to_base_k(n, 3)
if len(d3) < 5 or d3 != d3[::-1]:
return False
d7 = to_base_k(n, 7)
if len(set(d7)) != len(d7):
return False
dsum = sum(int(c) for c in str(n))
if not all(dsum % i != 0 for i in range(2, dsum)):
return False
if not all(n % i != 0 for i in range(2, int(n**0.5) + 1)):
return False
return True
except:
return False
def mystery(x):
try:
n = int(x)
if n <= 1:
return False
if not all(n % i != 0 for i in range(2, int(n**0.5) + 1)):
return False
def is_happy(num):
seen = set()
while num != 1 and num not in seen:
seen.add(num)
num = sum(int(d)**2 for d in str(num))
return num == 1
if not is_happy(n):
return False
def to_base(num, k):
if num == 0: return [0]
d = []
while num > 0:
d.append(num % k)
num //= k
return d
d2 = to_base(n, 2)
if d2 != d2[::-1]:
return False
d5 = to_base(n, 5)
if len(d5) != 3 or sum(d5) != 3:
return False
dsum = sum(int(c) for c in str(n))
if dsum % 3 != 1:
return False
if len(str(n)) % 2 != 0:
return False
return True
except:
return False
def mystery(x):
try:
import math
n = int(x)
if n <= 0:
return False
# Condition 1: n must be a perfect square
sq = int(math.isqrt(n))
if sq * sq != n:
return False
# Condition 2: the square root of n must be prime
p = sq
if p < 2:
return False
if not all(p % i != 0 for i in range(2, int(p**0.5) + 1)):
return False
# Condition 3: n represented in base 8 must be a palindrome
d8 = []
tmp = n
while tmp > 0:
d8.append(tmp % 8)
tmp //= 8
if d8 != d8[::-1]:
return False
# Condition 4: the sum of decimal digits of n must itself be prime
ds = sum(int(c) for c in str(n))
if ds < 2:
return False
if not all(ds % i != 0 for i in range(2, int(ds**0.5) + 1)):
return False
return True
except:
return False
def mystery(x):
try:
if not isinstance(x, str):
return False
if len(x) != 5:
return False
o = [ord(c) for c in x]
if any(not (97 <= oi <= 122) for oi in o):
return False
if sum(o) % 17 != 15:
return False
s = 0
for i in range(5):
s += o[i] * (i + 1)
if s != 1595:
return False
p = 1
for oi in o:
p = (p * oi) % 10007
if p != 3884:
return False
if o[4] - o[0] != 15:
return False
if o[2] % 4 != 0:
return False
if sum(oi**2 for oi in o) % 100 != 19:
return False
if o[4] != o[3] + 13:
return False
return True
except:
return False
def mystery(x):
try:
import math
n = int(x)
if n <= 3:
return False
r, t = [], n
while t:
r.append(t % 6)
t //= 6
if len(r) < 3 or r != r[::-1]:
return False
f, d, m = [], 2, n
while d * d <= m:
while m % d == 0:
f.append(d)
m //= d
d += 1
if m > 1:
f.append(m)
if len(f) != 2 or f[0] == f[1]:
return False
s = sum(int(c) for c in str(n))
q = int(math.isqrt(s))
if q * q != s or s <= 1:
return False
if (f[0] + f[1]) % 7 != 0:
return False
if n % 11 != 2:
return False
return True
except:
return False
def mystery(x):
try:
if not isinstance(x, str):
return False
if len(x) != 6:
return False
o = [ord(c) for c in x]
if any(not (97 <= oi <= 122) for oi in o):
return False
if len(set(o)) != 6:
return False
if sum(o) % 19 != 9:
return False
s = 0
for i in range(6):
s += o[i] * (i + 1)
if s != 2333:
return False
p = 1
for oi in o:
p = (p * oi) % 10007
if p != 1969:
return False
if (o[0] * o[5]) % 17 != 12:
return False
if o[4] - o[3] != 7:
return False
if sum(oi**2 for oi in o) % 100 != 78:
return False
if o[1] % 11 != 0:
return False
return True
except:
return False
def mystery(x):
try:
if not isinstance(x, str):
return False
if len(x) != 6:
return False
o = [ord(c) for c in x]
if any(not (97 <= oi <= 122) for oi in o):
return False
if len(set(o)) != 6:
return False
if sum(o) % 7 != 1:
return False
s = 0
for i in range(6):
s += o[i] * (i + 1)
if s != 2384:
return False
p = 1
for oi in o:
p = (p * oi) % 10007
if p != 4425:
return False
if o[2] - o[1] != 7:
return False
if o[3] % 7 != 0:
return False
if sum(oi**2 for oi in o) % 100 != 59:
return False
xv = 0
for oi in o:
xv ^= oi
if xv != 3:
return False
return True
except:
return False
def mystery(x):
try:
if not isinstance(x, str):
return False
if len(x) != 6:
return False
o = [ord(c) for c in x]
if any(not (97 <= oi <= 122) for oi in o):
return False
if len(set(o)) != 6:
return False
if sum(o) % 19 != 2:
return False
s = 0
for i in range(6):
s += o[i] * (i + 1)
if s != 2322:
return False
p = 1
for oi in o:
p = (p * oi) % 10007
if p != 2027:
return False
if o[0] - o[5] != 1:
return False
if o[2] % 9 != 0:
return False
if sum(oi**2 for oi in o) % 100 != 31:
return False
xv = 0
for oi in o:
xv ^= oi
if xv != 17:
return False
if (o[1] * o[3]) % 23 != 11:
return False
return True
except:
return False