def mystery(x):
try:
n = int(x)
if not (1000 <= n <= 9999):
return False
except ValueError:
return False
s = str(n).zfill(4)
desc = ''.join(sorted(s, reverse=True))
asc = ''.join(sorted(s))
diff = int(desc) - int(asc)
return diff == 6174
def mystery(x):
try:
n = int(x)
if n < 10:
return False
z = n
k = 0
while z >= 10:
p = 1
for c in str(z):
p *= int(c)
z = p
k += 1
return k == 5 and n % 97 == 0
except:
return False
def mystery(x):
try:
n = int(x)
if n < 10:
return False
z = n
k = 0
while z >= 10:
p = 1
for c in str(z):
p *= int(c)
z = p
k += 1
return k == 4 and n % 97 == 0
except:
return False
def mystery(x):
try:
n = int(x)
if not (100 <= n <= 9999):
return False
k = n
steps = 0
while k != 1:
k = k // 2 if k % 2 == 0 else 3 * k + 1
steps += 1
if steps > 1000000:
return False
ds = sum(int(c) for c in str(n))
return steps == ds ** 2
except:
return False
def mystery(x):
try:
n = int(x)
if not (1000 <= n <= 9999):
return False
def is_prime(m):
if m <= 1:
return False
if m <= 3:
return True
if m % 2 == 0 or m % 3 == 0:
return False
i = 5
while i * i <= m:
if m % i == 0 or m % (i + 2) == 0:
return False
i += 6
return True
if not is_prime(n):
return False
s = str(n)
base9 = 0
for c in s:
d = int(c)
if d >= 9:
return False
base9 = base9 * 9 + d
return base9 > 1 and is_prime(base9)
except ValueError:
return False
def mystery(x):
try:
n = int(x)
if not (10000 <= n <= 99999):
return False
def is_prime(m):
if m < 2:
return False
if m == 2:
return True
if m % 2 == 0:
return False
i = 3
while i * i <= m:
if m % i == 0:
return False
i += 2
return True
if not is_prime(n):
return False
s = sum(int(d) ** 3 for d in str(n))
if not is_prime(s):
return False
r = n % s
root = int(r ** 0.5)
if root * root != r:
return False
return r == 0 or is_prime(root)
except:
return False
def mystery(x):
try:
n = int(x)
if not (100000 <= n <= 166666):
return False
except ValueError:
return False
s = str(n)
if len(s) != 6:
return False
sorted_s = sorted(s)
for k in range(2, 7):
m = k * n
t = str(m)
if len(t) != 6 or sorted(t) != sorted_s:
return False
return True
def mystery(x):
try:
n = int(x)
if not (1000 <= n <= 9999):
return False
s = str(n)
def is_prime(m):
if m < 2: return False
if m == 2: return True
if m % 2 == 0: return False
i = 3
while i * i <= m:
if m % i == 0: return False
i += 2
return True
# Condition 1: n is prime
if not is_prime(n):
return False
# Condition 2: sum of all consecutive two-digit substrings is prime
pairs_sum = sum(int(s[i:i+2]) for i in range(len(s) - 1))
if not is_prime(pairs_sum):
return False
# Condition 3: product of digits equals (last two digits) - 1
prod = 1
for c in s:
prod *= int(c)
if prod != (n % 100) - 1:
return False
# Condition 4: sum of cubes of digits is prime
cube_sum = sum(int(c) ** 3 for c in s)
if not is_prime(cube_sum):
return False
return True
except:
return False
def mystery(x):
try:
n = int(x)
if n < 10:
return False
z = n
k = 0
while z >= 10:
p = 1
for c in str(z):
p *= int(c)
z = p
k += 1
return k == 4 and n % 113 == 0
except:
return False
def mystery(x):
try:
n = int(x)
if not (1000 <= n <= 9999):
return False
def is_prime(m):
if m < 2: return False
if m == 2: return True
if m % 2 == 0: return False
i = 3
while i * i <= m:
if m % i == 0: return False
i += 2
return True
s = str(n)
for length in range(1, len(s) + 1):
for start in range(len(s) - length + 1):
sub = int(s[start:start + length])
if sub != 1 and not is_prime(sub):
return False
return True
except:
return False