def mystery(x):
if not isinstance(x, int) or not (10**15 <= x < 10**16):
return False
if (x + 864197532) % 987654321 != 0:
return False
h = (x ^ (x >> 17)) * 0x517cc1b727220a95
h &= 0xFFFFFFFFFFFFFFFF
return (h ^ (h >> 31)) == 0xb7616110b8f43358
def mystery(x):
if not isinstance(x, str) or len(x) != 81:
return False
s = "".join(chr(ord(char) ^ 1) for char in x)
clues = "ME T A PCM CI A I A EU I E PT N A A NI I PC M I TC"
for i in range(81):
if clues[i] != ' ' and s[i] != clues[i]:
return False
rows = [s[i:i+9] for i in range(0, 81, 9)]
cols = [s[i::9] for i in range(9)]
boxes = [s[i*27+j*3:i*27+j*3+3] + s[i*27+j*3+9:i*27+j*3+12] + s[i*27+j*3+18:i*27+j*3+21] for i in range(3) for j in range(3)]
return all(set(g) == set("PNEUMATIC") for g in rows + cols + boxes)
def mystery(x):
if not isinstance(x, str) or len(x) != 8:
return False
# Extract Unicode code points
d = [ord(c) for c in x]
# A non-linear mixing step using an XOR chain
# Each value is combined with the next to create a new sequence
for i in range(7):
d[i] ^= d[i+1]
# The mixed values are treated as coefficients of a polynomial:
# P(z) = d[0] + d[1]*z + d[2]*z^2 + ... + d[7]*z^7
# This polynomial is evaluated at points z = 1, 2, ..., 8 in the field GF(257)
res = []
for i in range(1, 9):
v = sum(d[j] * pow(i, j, 257) for j in range(8)) % 257
res.append(v)
# Check the resulting evaluations against the target sequence
return res == [218, 173, 172, 175, 128, 205, 36, 26]
def mystery(x):
if not isinstance(x, str) or len(x) != 64:
return False
Q = {'W': 2, 'O': 3, 'L': 5, 'F': 7, 'R': 11, 'A': 13, 'M': 17, 'S': 19}
try:
V = [Q[c] for c in x]
except KeyError:
return False
def check(indices):
p = 1
for i in indices:
p *= V[i]
return p == 9699690
for i in range(8):
if not check(range(i*8, i*8+8)): return False
if not check(range(i, 64, 8)): return False
for i in range(4):
for j in range(2):
if not check([r*8+c for r in range(i*2, i*2+2) for c in range(j*4, j*4+4)]):
return False
C = [
(0, 'WOLFRAMS'),
(8, 'RAMS'),
(16, 'OLFWAMSR'),
(24, 'AMSROLFW'),
(32, 'LFWOMSRA'),
(56, 'SRAMFWOL')
]
for idx, s in C:
if x[idx:idx+len(s)] != s:
return False
return True
def mystery(x):
if not isinstance(x, str) or len(x) != 12 or not x.isdigit():
return False
# Part 1: Recursive additive check
# We treat the string as six 2-digit numbers
v = [int(x[i:i+2]) for i in range(0, 12, 2)]
# Each number (after the first two) must be the modular sum of the previous two
if any(v[i] != (v[i-1] + v[i-2]) % 100 for i in range(2, 6)):
return False
# Part 2: Statistical constraints
# The sum and product of these six integers must match specific targets
if sum(v) != 348 or (v[0] * v[1]) != 1656:
return False
# Part 3: Block-wise product constraint
# We partition the string into three 4-digit integers and check their product
m = [int(x[i:i+4]) for i in range(0, 12, 4)]
return (m[0] * m[1] * m[2]) == 141354223596
def mystery(x):
if not isinstance(x, str) or len(x) > 38:
return False
tape = [0] * 100
ptr = 0
out = ""
loops = {}
stack = []
for i, c in enumerate(x):
if c == '[':
stack.append(i)
elif c == ']':
if not stack:
return False
start = stack.pop()
loops[start] = i
loops[i] = start
if stack:
return False
pc = 0
ticks = 0
while pc < len(x) and ticks < 5000:
c = x[pc]
if c == '>': ptr = (ptr + 1) % 100
elif c == '<': ptr = (ptr - 1) % 100
elif c == '+': tape[ptr] = (tape[ptr] + 1) % 256
elif c == '-': tape[ptr] = (tape[ptr] - 1) % 256
elif c == '.': out += chr(tape[ptr])
elif c == '[' and tape[ptr] == 0: pc = loops[pc]
elif c == ']' and tape[ptr] != 0: pc = loops[pc]
pc += 1
ticks += 1
return out == "Z3"
def mystery(x):
if not isinstance(x, str) or len(x) != 16:
return False
# Check for 16 unique characters from 'A' to 'P'
if len(set(x)) != 16 or any(ord(c) < 65 or ord(c) > 80 for c in x):
return False
v = [ord(c) for c in x]
# Calculate sums of each row, column, and the two main diagonals
# For a 16-character string representing a 4x4 magic square
rows = [sum(v[i*4 : i*4+4]) for i in range(4)]
cols = [sum(v[i::4]) for i in range(4)]
diags = [sum(v[i*5] for i in range(4)), sum(v[i*3+3] for i in range(4))]
# All sums must equal the magic constant for the character set 'A' through 'P'
if any(s != 290 for s in rows + cols + diags):
return False
# Geometric constraint on the product of the four corner elements
if v[0] * v[3] * v[12] * v[15] != 27227200:
return False
# Permutation-specific weighted sum constraint
return sum((i + 1) * v[i] for i in range(16)) == 9860
def mystery(x):
if not isinstance(x, str) or len(x) > 43:
return False
tape = [0] * 300
ptr = 0
out = ""
loops = {}
stack = []
for i, c in enumerate(x):
if c == '[':
stack.append(i)
elif c == ']':
if not stack:
return False
start = stack.pop()
loops[start] = i
loops[i] = start
if stack:
return False
pc = 0
ticks = 0
while pc < len(x) and ticks < 10000:
c = x[pc]
if c == '>': ptr = (ptr + 1) % 300
elif c == '<': ptr = (ptr - 1) % 300
elif c == '+': tape[ptr] = (tape[ptr] + 1) % 256
elif c == '-': tape[ptr] = (tape[ptr] - 1) % 256
elif c == '.': out += chr(tape[ptr])
elif c == '[' and tape[ptr] == 0: pc = loops[pc]
elif c == ']' and tape[ptr] != 0: pc = loops[pc]
pc += 1
ticks += 1
return out == "aeimquy"
def mystery(x):
if not isinstance(x, str) or len(x) != 16:
return False
# Check if x is a permutation of a specific set of 16 characters
required_chars = ['1', '2', '3', '4', '5', 'F', 'H', 'I', 'N', 'N', 'O', 'P', 'S', 'T', 'U', 'Y']
if sorted(x) != required_chars:
return False
v = [ord(c) for c in x]
# Constraint 1: Row-wise XOR sums for each 4-character block
rows_xor = [v[i*4] ^ v[i*4+1] ^ v[i*4+2] ^ v[i*4+3] for i in range(4)]
if rows_xor != [21, 27, 108, 0]:
return False
# Constraint 2: Column-wise arithmetic sums in the 4x4 grid
cols_sum = [sum(v[i::4]) for i in range(4)]
if cols_sum != [279, 303, 287, 257]:
return False
# Constraint 3: Arithmetic sums of the two main diagonals
if (v[0] + v[5] + v[10] + v[15]) != 289 or (v[3] + v[6] + v[9] + v[12]) != 280:
return False
# Constraint 4: A specific weighted sum to ensure a unique permutation
return sum((i + 1) * v[i] for i in range(16)) == 8754
def mystery(x):
# x must be a list of exactly 100 elements
if type(x) is not list or len(x) != 100:
return False
# Must be a permutation of 0 through 99
if len(set(x)) != 100 or min(x) != 0 or max(x) != 99:
return False
# Diagonal constraints (N-Queens)
if len(set(i + x[i] for i in range(100))) != 100:
return False
if len(set(i - x[i] for i in range(100))) != 100:
return False
# Geometric structure constraints
if sum(abs(x[i] - x[i+1]) for i in range(99)) != 295:
return False
# Weighted positional constraints
if sum(i * x[i] for i in range(100)) != 285425:
return False
# Adjacent product constraints
if sum(x[i] * x[i+1] for i in range(99)) != 318451:
return False
return True