def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if x <= 0:
return False
s = str(x)
if len(s) != 10:
return False
if len(set(s)) != 10:
return False
if x % 11 != 0:
return False
digits = [int(c) for c in s]
if digits[0] >= digits[-1]:
return False
if sum(digits[:5]) != 25:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if x <= 0:
return False
s = str(x)
if len(s) != 10:
return False
if len(set(s)) != 10:
return False
for i in range(1, 11):
prefix = int(s[:i])
if prefix % i != 0:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if x <= 0:
return False
s = str(x)
if len(s) != 9:
return False
if set(s) != set("123456789"):
return False
a, b, c = int(s[:3]), int(s[3:6]), int(s[6:])
if a + b != c:
return False
if a < b:
return False
if a % 91 != 0:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if x <= 0:
return False
s = str(x)
if len(s) != 10:
return False
if len(set(s)) != 10:
return False
if x % 100 != 90:
return False
digits = [int(c) for c in s]
if sum(digits[:5]) != 23:
return False
if sum(digits[::2]) != 25:
return False
if digits[0] <= digits[-1]:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if x <= 0:
return False
s = str(x)
if len(s) != 6:
return False
if s != s[::-1]:
return False
digits = [int(c) for c in s]
if sum(digits) != 30:
return False
if x % 77 != 0:
return False
A, B, C = digits[0], digits[1], digits[2]
if B <= A or B <= C:
return False
if A * C != 0:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if x <= 0:
return False
s = str(x)
if len(s) != 10:
return False
if len(set(s)) != 10:
return False
if int(s[1:4]) % 2 != 0:
return False
if int(s[2:5]) % 3 != 0:
return False
if int(s[3:6]) % 5 != 0:
return False
if int(s[4:7]) % 7 != 0:
return False
if int(s[5:8]) % 11 != 0:
return False
if int(s[6:9]) % 13 != 0:
return False
if int(s[7:10]) % 17 != 0:
return False
return True
def mystery(x):
if not isinstance(x, str):
return False
if len(x) != 8:
return False
if not x.isalpha() or not x.islower():
return False
# Shift each letter by its (0-indexed) position
shifted = ''.join(chr((ord(c) - ord('a') + i) % 26 + ord('a')) for i, c in enumerate(x))
if shifted != shifted[::-1]:
return False
# Letter values (a=1..z=26) sum to exactly 100
if sum(ord(c) - ord('a') + 1 for c in x) != 100:
return False
# All 8 letters distinct
if len(set(x)) != 8:
return False
# First letter strictly precedes last alphabetically
if x[0] >= x[-1]:
return False
return True
def mystery(x):
if not isinstance(x, str):
return False
if len(x) != 7:
return False
if not x.isalpha() or not x.islower():
return False
if len(set(x)) != 7:
return False
shifted = ''.join(chr((ord(c) - ord('a') + i) % 26 + ord('a')) for i, c in enumerate(x))
if shifted != shifted[::-1]:
return False
if sum(ord(c) - ord('a') + 1 for c in x) != 100:
return False
if x[0] <= x[-1]:
return False
letter_vals = [ord(c) - ord('a') + 1 for c in x]
if sum(letter_vals[::2]) != 52:
return False
if letter_vals[2] + letter_vals[5] != 25:
return False
return True
def mystery(x):
if not isinstance(x, int) or isinstance(x, bool):
return False
if x <= 0:
return False
s = str(x)
if len(s) != 8:
return False
if len(set(s)) != 8:
return False
if x % 77 != 0:
return False
digits = [int(c) for c in s]
for i in range(4):
if digits[i] + digits[7-i] != 9:
return False
if digits[0] >= digits[1]:
return False
if digits[2] % 2 != 0:
return False
if digits[1] * digits[3] != 6:
return False
return True
def mystery(x):
if not isinstance(x, str):
return False
if len(x) != 8:
return False
if not x.isalpha() or not x.islower():
return False
if len(set(x)) != 8:
return False
shifted = ''.join(chr((ord(c) - ord('a') + i) % 26 + ord('a')) for i, c in enumerate(x))
if shifted != shifted[::-1]:
return False
letter_vals = [ord(c) - ord('a') + 1 for c in x]
if sum(letter_vals) != 154:
return False
if x[0] <= x[-1]:
return False
if sum(letter_vals[:4]) != 85:
return False
if sum(letter_vals[::2]) != 79:
return False
if letter_vals[3] % 5 != 4:
return False
if letter_vals[2] <= letter_vals[5]:
return False
if letter_vals[0] + letter_vals[7] != 29:
return False
if letter_vals[4] % 2 != 1:
return False
return True