def mystery(x):
try:
n = int(x)
except ValueError:
return False
s = str(n)
if len(s) != 4:
return False
power = len(s)
total = sum(int(d) ** power for d in s)
return total == n
def mystery(x):
try:
n = int(x)
except ValueError:
return False
if n < 10:
return False
d = [int(c) for c in str(n)]
while True:
s = sum(d)
if s == n: return True
if s > n: return False
d = d[1:] + [s]
def mystery(x):
try:
n = int(x)
except ValueError:
return False
s = str(n)
if not s:
return False
t = str(n * 2)
if len(t) != len(s):
return False
return t in (s + s)
def mystery(x):
try:
n = int(x)
except ValueError:
return False
def fact(k):
if k == 0 or k == 1: return 1
r = 1
for i in range(2, k + 1):
r *= i
return r
total = 0
m = n
while m > 0:
total += fact(m % 10)
m //= 10
return total == n and n > 100
def mystery(x):
try:
n = int(x)
except ValueError:
return False
s = str(n)
if len(s) < 4:
return False
sq = str(n * n)
return sq.endswith(s)
def mystery(x):
try:
n = int(x)
except ValueError:
return False
def weird_pow(b, e):
r = 1
while e > 0:
r *= b
e -= 1
return r
total = 0
m = n
while m > 0:
d = m % 10
total += weird_pow(d, d)
m //= 10
return total == n and n > 1000
def mystery(x):
try:
n = int(x)
except ValueError:
return False
if n < 1000:
return False
count = 0
max_k = int(n ** (1/3)) + 2
for i in range(1, max_k):
i3 = i ** 3
if i3 >= n:
break
for j in range(i + 1, max_k):
j3 = j ** 3
if i3 + j3 > n:
break
if i3 + j3 == n:
count += 1
if count >= 2:
return True
return False
def mystery(x):
try:
n = int(x)
except ValueError:
return False
def weird_mult(a, b):
result = 0
while b > 0:
result += a
b -= 1
return result
def weird_cube(k):
return weird_mult(weird_mult(k, k), k)
cubes = []
k = 1
while True:
c = weird_cube(k)
if c >= n:
break
cubes.append(c)
k += 1
count = 0
for i in range(len(cubes)):
i3 = cubes[i]
for j in range(i + 1, len(cubes)):
total = i3 + cubes[j]
if total == n:
count += 1
if count >= 3:
return True
if total > n:
break
return False
def mystery(x):
try:
n = int(x)
except ValueError:
return False
def divisor_sum(m):
if m < 2:
return 0
total = 1
sqrt_m = int(m ** 0.5) + 1
for i in range(2, sqrt_m):
if m % i == 0:
total += i
j = m // i
if j != i and j != m:
total += j
return total
s = divisor_sum(n)
if s == n or s < n: # Exclude perfect numbers and cases where s < n to avoid trivial
return False
t = divisor_sum(s)
return t == n
def mystery(x):
try:
n = int(x)
except ValueError:
return False
if n < 10000:
return False
def weird_mult(a, b):
res = 0
while b > 0:
res += a
b -= 1
return res
def weird_sqrt(m):
s = 0
while weird_mult(s + 1, s + 1) <= m:
s += 1
return s
def divisor_sum(m):
if m < 2:
return 0
total = 1
sqrtm = weird_sqrt(m) + 1
for i in range(2, sqrtm):
if m % i == 0:
total += i
j = m // i
if j != i and j != m:
total += j
return total
return divisor_sum(n) == n