def mystery(x):
if isinstance(x, str):
try:
x = int(x)
except:
return False
if not isinstance(x, int) or x < 0:
return False
seen = set()
while x != 1 and x not in seen:
seen.add(x)
x = sum(int(d) ** 2 for d in str(x))
return x == 1
def mystery(x):
if isinstance(x, str):
try:
x = int(x)
except:
return False
if not isinstance(x, int) or x <= 0:
return False
s = str(x)
for i, d in enumerate(s):
if s.count(str(i)) != int(d):
return False
return True
def mystery(x):
if isinstance(x, str):
try:
x = int(x)
except:
return False
if not isinstance(x, int) or x <= 0:
return False
# Count the number of divisors
divisor_count = 0
for i in range(1, x + 1):
if x % i == 0:
divisor_count += 1
# Calculate the product of digits
digit_product = 1
for digit in str(x):
digit_product *= int(digit)
# Return True if divisor count equals digit product
return divisor_count == digit_product
def mystery(x):
if isinstance(x, str):
try:
x = int(x)
except:
return False
if not isinstance(x, int) or x <= 1:
return False
def f(n):
count = 0
while n:
count += n & 1
n >>= 1
return count
def g(n):
result = 1
for c in str(n):
result *= int(c)
return result
def h(n):
if n < 2:
return False
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True
return h(x) and f(x) == g(x)
def mystery(x):
if isinstance(x, str):
try:
x = int(x)
except:
return False
if not isinstance(x, int) or x < 0:
return False
def factorial(n):
if n <= 1:
return 1
result = 1
for i in range(2, n + 1):
result *= i
return result
digit_factorial_sum = sum(factorial(int(d)) for d in str(x))
return x == digit_factorial_sum
def mystery(x):
if isinstance(x, str):
try:
x = int(x)
except:
return False
if not isinstance(x, int) or x <= 9:
return False
s = str(x)
# Unnamed check 1
acc = sum(int(s[i]) ** (i + 1) for i in range(len(s)))
# Unnamed check 2
sm = sum(int(c) for c in s)
sq = int((x + sm) ** 0.5)
return acc == x and sq * sq == x + sm
def mystery(x):
if isinstance(x, str):
try:
x = int(x)
except:
return False
if not isinstance(x, int) or x <= 9:
return False
digit_product = 1
digit_sum = 0
for d in str(x):
digit_product *= int(d)
digit_sum += int(d)
return digit_product == digit_sum
def mystery(x):
if not isinstance(x, str):
return False
if len(x) < 2:
return False
def a(n):
if n < 2: return False
for i in range(2, int(n**0.5) + 1):
if n % i == 0: return False
return True
def b(s):
try:
return int(s)
except:
return None
def c(n):
return sum(int(d) for d in str(n))
v1 = b(x)
v2 = b(x[::-1])
if v1 is None or v2 is None:
return False
p = v1 * v2
ds = c(p)
r = int(ds ** 0.5)
return a(v1) and a(v2) and r * r == ds
def mystery(x):
if isinstance(x, str):
try:
x = int(x)
except:
return False
if not isinstance(x, int) or x <= 10:
return False
# Check if x is a triangular number: x = n(n+1)/2
discriminant = 1 + 8 * x
sqrt_disc = int(discriminant ** 0.5)
if sqrt_disc * sqrt_disc != discriminant:
return False
n = (-1 + sqrt_disc) // 2
if n * (n + 1) // 2 != x:
return False
# Check if digit sum equals the index n
digit_sum = sum(int(d) for d in str(x))
return digit_sum == n
def mystery(x):
if not isinstance(x, str):
return False
s = x.lower().replace(' ', '')
if not s.isalpha() or len(s) < 2:
return False
m = [ord(c) - 96 for c in s]
# Check A
total = sum(m)
r = int(total ** 0.5)
if r * r != total:
return False
# Check B
prod = 1
for v in m:
prod *= v
if prod % len(s) != 0:
return False
# Check C
vc = sum(1 for c in s if c in 'aeiou')
if vc < 2:
return False
k = 2
while k * k <= vc:
if vc % k == 0:
return False
k += 1
# Check D
ln = len(s)
if int(ln ** 0.5) ** 2 != ln:
return False
return True