import math
def mystery(x):
"""
This function takes a value x (either string or number) and returns a boolean.
"""
if not isinstance(x, (int, str)):
return False
try:
num_val = int(x)
except (ValueError, TypeError):
return False
if num_val <= 0:
return False
# Helper to get distinct prime factors
def _get_distinct_prime_factors(n):
factors = set()
d = 2
temp = n
while d * d <= temp:
if temp % d == 0:
factors.add(d)
while temp % d == 0:
temp //= d
d += 1
if temp > 1:
factors.add(temp)
return factors
# Condition 1: Check the length of the number's string representation
if len(str(num_val)) != 9:
return False
# Condition 2: Calculate the sum of its digits
sum_of_digits = sum(int(digit) for digit in str(num_val))
# Condition 3: Calculate the count of its distinct prime factors
distinct_prime_factors_count = len(_get_distinct_prime_factors(num_val))
# Final mysterious condition
return sum_of_digits * distinct_prime_factors_count == 90
def mystery(x):
if isinstance(x, int):
s = str(x)
elif isinstance(x, str):
s = x
else:
return False
if len(s) != 3:
return False
xor_val = 0
for ch in s:
xor_val ^= ord(ch)
return xor_val == 42
import math
def mystery(x):
"""
This function takes a value x (either string or number) and returns a boolean.
"""
if not isinstance(x, (int, str)):
return False
s_val = ""
num_val = 0
if isinstance(x, int):
s_val = str(x)
num_val = x
elif isinstance(x, str):
# A string must be convertible to an integer to proceed.
try:
num_val = int(x)
s_val = x # Keep original string for ascii_sum
except ValueError:
return False
# Condition 1: The numerical value must be positive.
if num_val <= 0:
return False
# Condition 2: The length of the number's string representation must be exactly 7 digits.
if len(s_val) != 7:
return False
# Helper function to check for primality.
def _is_prime(n):
if n < 2:
return False
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
# Condition 3: The sum of its digits must be a prime number.
sum_of_digits = sum(int(digit) for digit in s_val)
if not _is_prime(sum_of_digits):
return False
# Condition 4: The count of set bits (1s) in its binary representation must be exactly 1.
# This implies the number is a power of 2.
binary_repr = bin(num_val)[2:] # Remove "0b" prefix
if binary_repr.count('1') != 1:
return False
# Condition 5: The sum of the ASCII values of the characters in its string representation
# must be strictly between 365 and 370 (exclusive).
# This implicitly requires the string to consist only of digits '0'-'9'.
ascii_sum = sum(ord(c) for c in s_val)
if not (365 < ascii_sum < 370): # This means ascii_sum must be 366, 367, 368, or 369.
return False
return True
def mystery(x):
if isinstance(x, int):
s = str(x)
elif isinstance(x, str):
s = x
else:
return False
if len(s) != 6:
return False
# Condition 1: Weighted sum based on position and ASCII value
checksum = 0
for i, ch in enumerate(s):
checksum += (i + 1) * ord(ch)
if checksum != 1729:
return False
# Condition 2: XOR of all characters must be 0
xor_val = 0
for ch in s:
xor_val ^= ord(ch)
if xor_val != 0:
return False
return True
import math
import string
def mystery(x):
"""
This function takes a value x (either string or number) and returns a boolean.
"""
s = ""
if isinstance(x, int):
s = str(x)
elif isinstance(x, str):
s = x
else:
return False
# Condition 1: The string representation must have a length of exactly 7 characters.
if len(s) != 7:
return False
# Condition 2: All characters in the string must be uppercase alphanumeric (0-9, A-Z).
# This also ensures it's valid for base-36 conversion.
for char_val in s:
if not ('0' <= char_val <= '9' or 'A' <= char_val <= 'Z'):
return False
# Condition 3: The string must be a palindrome (reads the same forwards and backwards).
if s != s[::-1]:
return False
# Condition 4: Treat the string as a number in base-36 and convert it to its decimal value.
try:
num_val_base36 = int(s, 36)
except ValueError:
# This should ideally be caught by Condition 2, but acts as a safeguard.
return False
# Condition 5: The resulting decimal value must be a perfect square.
# We use math.isqrt for efficient integer square root.
sqrt_val = math.isqrt(num_val_base36)
if sqrt_val * sqrt_val != num_val_base36:
return False
# Condition 6: The sum of the ASCII values of all characters in the string must be exactly 403.
ascii_sum = sum(ord(c) for c in s)
if ascii_sum != 403:
return False
return True
def mystery(x):
if isinstance(x, int):
s = str(x)
elif isinstance(x, str):
s = x
else:
return False
if len(s) != 5:
return False
# Condition 1: Position-weighted sum of ASCII values
weighted_sum = sum(ord(ch) * (i + 1) for i, ch in enumerate(s))
if weighted_sum != 799:
return False
# Condition 2: Product of all ASCII values mod 1000
prod = 1
for ch in s:
prod *= ord(ch)
if prod % 1000 != 500:
return False
return True
def mystery(x):
"""
This function takes a value x (either string or number) and returns a boolean.
"""
if not isinstance(x, str):
return False
# Condition 1: The string must have a length of exactly 6 characters.
if len(x) != 6:
return False
ascii_values = []
vowel_count = 0
vowels = {'A', 'E', 'I', 'O', 'U'}
for char_val in x:
# Condition 2: All characters must be uppercase English letters (A-Z).
if not ('A' <= char_val <= 'Z'):
return False
ascii_values.append(ord(char_val))
# Condition 3: The string must contain exactly 3 vowels (A, E, I, O, U).
if char_val in vowels:
vowel_count += 1
if vowel_count != 3:
return False
# Condition 4: The sum of the ASCII values of the characters must be exactly 450.
sum_ascii = sum(ascii_values)
if sum_ascii != 450:
return False
# Condition 5: The bitwise XOR sum of the ASCII values of the characters must be exactly 10.
xor_sum_val = 0
for val in ascii_values:
xor_sum_val ^= val
if xor_sum_val != 10:
return False
# Condition 6: The product of the ASCII values of the characters must be divisible by 1000.
# (Note: 1000 = 2^3 * 5^3)
prod_ascii = 1
for val in ascii_values:
prod_ascii *= val
if prod_ascii % 1000 != 0:
return False
return True
def mystery(x):
if isinstance(x, int):
s = str(x)
elif isinstance(x, str):
s = x
else:
return False
if len(s) != 4:
return False
if not all(c.isdigit() for c in s):
return False
try:
num = int(s)
except:
return False
# Check various properties
digits = [int(c) for c in s]
# Hidden condition 1
if num % 17 != 3:
return False
# Hidden condition 2
if sum(digits) != 13:
return False
# Hidden condition 3
prod = 1
for d in digits:
prod *= d
if prod != 24:
return False
# Hidden condition 4
if digits[0] == digits[-1]:
return False
return True
import math
def mystery(x):
"""
This function takes a value x (either string or number) and returns a boolean.
"""
if not isinstance(x, str):
return False
# Condition 1: The string must have a length of exactly 6 characters.
if len(x) != 6:
return False
# Condition 2: All characters must be digits ('0'-'9').
if not all(c.isdigit() for c in x):
return False
digits = [int(d) for d in x]
# Condition 3: The sum of its digits must be a perfect square. (Specifically 16)
sum_of_digits = sum(digits)
if sum_of_digits != 16:
return False
# Condition 4: The sum of the ASCII values of the characters must be exactly 304.
# (This is derived from sum_of_digits == 16: 6*ord('0') + sum_of_digits = 6*48 + 16 = 288 + 16 = 304)
ascii_values = [ord(c) for c in x]
if sum(ascii_values) != 304:
return False
# Condition 5: The sum of digits at odd positions (0, 2, 4) must equal the sum of digits at even positions (1, 3, 5).
# Both sums must be 8 (since the total sum of digits is 16).
sum_odd_indices = digits[0] + digits[2] + digits[4]
sum_even_indices = digits[1] + digits[3] + digits[5]
if sum_odd_indices != 8 or sum_even_indices != 8:
return False
# Condition 6: The number of prime digits (2, 3, 5, 7) within the string must be exactly 3.
prime_digits = {2, 3, 5, 7}
prime_count = sum(1 for d in digits if d in prime_digits)
if prime_count != 3:
return False
# Condition 7: No two adjacent digits can be the same.
for i in range(len(digits) - 1):
if digits[i] == digits[i+1]:
return False
return True
def mystery(x):
if not isinstance(x, str):
return False
if len(x) != 7:
return False
# Must contain only lowercase letters
if not all('a' <= c <= 'z' for c in x):
return False
# Sum of ASCII values
if sum(ord(c) for c in x) != 700:
return False
# Must be a palindrome
if x != x[::-1]:
return False
# First character must be 'h'
if x[0] != 'h':
return False
return True