def mystery(x):
if not (isinstance(x, str) and len(x) == 16):
return False
try:
v = int(x, 16)
except ValueError:
return False
m = 0xFFFFFFFFFFFFFFFF
s = [0x5A1F8D42, 0x3C07E1B9, 0x6D4B2A85, 0x9E3779B9]
for i in range(64):
v = (v ^ (v << 13)) & m
v = (v ^ (v >> 17)) & m
v = (v ^ (v << 5)) & m
v = (v * 0x517cc1b727220a95 + 0xdeadbeef) & m
v = (v ^ s[i % 4]) & m
return v == 0xbe6975a5e3789073
def mystery(x):
if not isinstance(x, int):
return False
if x < 1 or x > 1000000:
return False
s = str(x)
total = 0
for digit_char in s:
d = int(digit_char)
factorial = 1
for i in range(1, d + 1):
factorial *= i
total += factorial
return x == total
def mystery(x):
if not isinstance(x, int) or not (0 <= x < 0x10000000000000000):
return False
# 64-bit mask and multiplier
m = 0xFFFFFFFFFFFFFFFF
a = 0x5851F42D4C957F2D
# Round 1: Linear congruential step and half-width XOR-shift
v = (x * a + 0xDEADBEEF) & m
v ^= (v >> 32)
# Round 2: Second linear congruential step and half-width XOR-shift
v = (v * a + 0x12345678) & m
v ^= (v >> 32)
return v == 0xA745582FCE177FC7
def mystery(x):
if not isinstance(x, int) or x < 0 or x > 10000:
return False
# Check if x is a perfect square
sqrt_x = int(x ** 0.5)
if sqrt_x * sqrt_x != x:
return False
# Check if the sum of digits is also a perfect square
digit_sum = sum(int(d) for d in str(x))
sqrt_sum = int(digit_sum ** 0.5)
return sqrt_sum * sqrt_sum == digit_sum
def mystery(x):
if not (isinstance(x, str) and len(x) == 10 and x.isdigit()):
return False
# Each digit from 0 to 9 must be present exactly once
if len(set(x)) != 10:
return False
# For every n from 1 to 10, the number formed by the
# first n digits must be divisible by n
for n in range(1, 11):
if int(x[:n]) % n != 0:
return False
return True
def mystery(x):
if not isinstance(x, int) or x < 0 or x > 10000:
return False
# Check if sum of cubes of digits equals the number
s = str(x)
if sum(int(d)**3 for d in s) != x:
return False
# Check if digit sum is a prime number
digit_sum = sum(int(d) for d in s)
if digit_sum < 2:
return False
for i in range(2, int(digit_sum**0.5) + 1):
if digit_sum % i == 0:
return False
return True
def mystery(x):
if not isinstance(x, int) or not (0 <= x < 0x10000000000000000):
return False
# 64-bit mask and multiplier (Knuth's MMIX)
m = 0xFFFFFFFFFFFFFFFF
a = 0x5851F42D4C957F2D
v = x
# Apply two rounds of reversible transformation
for _ in range(2):
v = (v ^ (v >> 32)) & m
v = (v * a) & m
# Final XOR-shift step
v = (v ^ (v >> 32)) & m
return v == 0xDEADBEEFCABDFBEF
def mystery(x):
if not isinstance(x, int) or x < 0 or x > 1000000:
return False
digit_sum = sum(int(d) for d in str(x))
return x == digit_sum ** 3
def mystery(x):
if not isinstance(x, int) or not (0 <= x < 0x100000000):
return False
# 32-bit mask and constants
m = 0xFFFFFFFF
a = 0x41c64e6d
c = 0x3039
v = x
# Three rounds of a reversible transformation
for i in range(3):
# Step 1: XOR-shift right (reversible)
v = (v ^ (v >> 16)) & m
# Step 2: Linear congruential step (reversible via modular inverse)
v = (v * a + c) & m
# Step 3: XOR-shift left (reversible)
v = (v ^ (v << 16)) & m
# Step 4: Modular addition (reversible)
v = (v + 0x7b) & m
return v == 0x20880087
def mystery(x):
if not isinstance(x, int) or x < 0 or x > 100000:
return False
square = x * x
s = str(square)
for i in range(1, len(s)):
left = int(s[:i])
right = int(s[i:])
if left + right == x:
return True
return False