def mystery(x):
# The input must be a specific integer within a reasonable range.
if not isinstance(x, int):
return False
if x < 0 or x > 1000000:
return False
# Transformation 1: A bitwise mapping
# This looks like a simple XOR, but it has a specific name in coding theory.
v = x ^ (x >> 1)
# Transformation 2: Modular Arithmetic
# We check if v satisfies a linear congruence: v * A = B (mod M)
multiplier = 87654321
modulus = 1000000009 # A large prime
target_remainder = 539504658
return (v * multiplier) % modulus == target_remainder
def mystery(x):
# The function accepts a single value x and returns True only for a very specific string.
# The implementation is intentionally obfuscated with a few harmless checks to disguise the real test.
if not isinstance(x, str):
return False
# Some red herrings: length and character checks that still allow the true solution.
if not (1 <= len(x) <= 1000):
return False
# allow common printable characters (doesn't rule out the real secret)
for ch in x:
if ord(ch) < 32 or ord(ch) > 126:
return False
import hashlib
# The real test: compute SHA-1 of the UTF-8 bytes and compare to a fixed hex digest.
# (This makes finding a solution a preimage-search problem for the given digest.)
digest = hashlib.sha1(x.encode('utf-8')).hexdigest()
target = "a9993e364706816aba3e25717850c26c9cd0d89d"
return digest == target
def mystery(x):
# The input must be a string of exactly 8 characters.
if not isinstance(x, str) or len(x) != 8:
return False
# Convert the string to a list of ASCII integer values.
# We will modify this state in place.
state = [ord(c) for c in x]
# A simple key schedule based on position.
keys = [2 * i + 1 for i in range(8)]
# Apply a mixing transformation.
# This loop runs once, processing the state from index 0 to 7.
# The transformation of each element depends on its right neighbor (wrapping around).
# Since we modify the array in place, the last element (index 7) will use the
# *already modified* value of the first element (index 0).
for i in range(8):
neighbor_idx = (i + 1) % 8
# Mixing operation:
# 1. Add the neighbor's value (modulo 256).
# 2. XOR with the key for this position.
val = (state[i] + state[neighbor_idx]) % 256
state[i] = val ^ keys[i]
# The resulting state must match this specific target sequence.
target = [195, 216, 228, 238, 212, 227, 216, 62]
return state == target
def mystery(x):
# The function accepts a single value and returns True only for a very specific string.
# It's written to look noisy and full of red herrings.
if not isinstance(x, str):
return False
# Harmless length filter to discourage trivial inputs
if not (1 <= len(x) <= 1000):
return False
# Only allow common printable ASCII (still allows the true answer)
for ch in x:
if ord(ch) < 32 or ord(ch) > 126:
return False
# A few noisy computations that do nothing to the real test:
# - a silly checksum
checksum = 0
for i, ch in enumerate(x):
checksum = ((checksum << 5) - checksum) + (ord(ch) ^ (i & 0xFF))
checksum &= 0xFFFFFFFF
# - a small obfuscated transformation (keeps options open but not decisive)
t = 0
for ch in x:
t = (t * 1315423911) ^ ord(ch)
t &= 0xFFFFFFFFFFFFFFFF
# The real test: SHA-256 of the UTF-8 bytes must match a fixed digest.
import hashlib
digest = hashlib.sha256(x.encode('utf-8')).hexdigest()
# This target digest is the SHA-256 of the hidden required string.
target = "d7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592"
# Final decision uses only the digest comparison; the rest was misdirection.
return digest == target
def mystery(x):
# The input must be a string of exactly 8 characters.
if not isinstance(x, str) or len(x) != 8:
return False
# Ensure standard byte-range characters to avoid ambiguity
if any(ord(c) > 255 for c in x):
return False
# Convert string to a mutable list of ASCII integers
s = [ord(c) for c in x]
# Apply a sequential transformation chain.
# The state is updated in place, creating a dependency on previously modified values.
for i in range(8):
# Identify the neighbor. For the last element, it wraps around to index 0.
# Crucially, since the loop proceeds from 0 to 7, when i=7,
# s[0] has ALREADY been modified in the first iteration (i=0).
neighbor = s[(i + 1) % 8]
# Operation:
# 1. XOR current value with neighbor
# 2. Add a constant (42)
# 3. Mask to 8 bits
# 4. Circular Rotate Left by 3 bits
val = (s[i] ^ neighbor) + 42
val &= 0xFF # Ensure byte range
# Rotate Left 3 bits
s[i] = ((val << 3) | (val >> 5)) & 0xFF
# The transformed state must match this specific sequence
target = [113, 105, 26, 89, 58, 129, 89, 74]
return s == target
def mystery(x):
# Accept only strings (this puzzles hides the real test among lots of noise).
if not isinstance(x, str):
return False
# Harmless constraints to discourage trivial binary inputs.
if not (1 <= len(x) <= 1024):
return False
for ch in x:
if ord(ch) < 32 or ord(ch) > 126:
return False
# --- Red herrings start ---
# A pointless byte-mangling that looks important but is unused in the final decision.
data = bytearray(x.encode('utf-8'))
# mix bytes in an in-place reversible-ish way (but result is never checked)
for i in range(len(data)):
j = (i * 7 + 13) % (len(data))
data[i], data[j] = (data[i] ^ 0xAA) & 0xFF, (data[j] ^ 0x55) & 0xFF
# a faux checksum that might lead you to try to invert it
chk = 0x12345678
for b in data:
chk = ((chk << 5) | (chk >> 27)) & 0xFFFFFFFF
chk ^= (b + 0x9e3779b9) & 0xFFFFFFFF
# a red herring mapping table (never used for the final test)
table = [(i * 2654435761) & 0xFFFFFFFF for i in range(256)]
mapped = [table[b] & 0xFF for b in data]
# a pseudo-random-looking integer derived from the string (also not decisive)
seed = 1469598103934665603
for b in mapped:
seed ^= b
seed = (seed * 1099511628211) & 0xFFFFFFFFFFFFFFFF
# --- Real test below (small and precise) ---
import hashlib
# The true gate is a single SHA-256 comparison of the UTF-8 bytes.
digest = hashlib.sha256(x.encode('utf-8')).hexdigest()
# The target digest is fixed; nothing else above affects the final check.
target = "2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824"
return digest == target
def mystery(x):
# The input must be a string of exactly 8 characters.
if not isinstance(x, str) or len(x) != 8:
return False
# Convert the string to a list of ASCII integer values.
vals = [ord(c) for c in x]
# Split the input into Left (L) and Right (R) halves.
# This setup suggests a Feistel network structure.
L = vals[:4]
R = vals[4:]
# We perform 2 rounds of transformation.
keys = [0xAA, 0x55]
for k in keys:
# The round function F(R):
# 1. Sum the values in the Right half.
# 2. Take the lower 8 bits.
# 3. XOR with the round key.
f_val = (sum(R) & 0xFF) ^ k
# Feistel update:
# New Right = Old Left XOR F(Old Right)
# New Left = Old Right
# Note: We apply the scalar f_val to every byte of L.
new_R = [v ^ f_val for v in L]
L = R
R = new_R
# The final state (Left concatenated with Right) must match this target.
target = [211, 246, 253, 253, 246, 243, 169, 183]
return (L + R) == target
def mystery(x):
# Accept only integers within a reasonable range
if not isinstance(x, int):
return False
if x < 2 or x > 10**7:
return False
# A few pointless-looking computations to add noise
# (these do not affect the final decision)
s = 0
a, b = 1, 1
for i in range(10):
a, b = b, a + b
s ^= (a * (i + 1)) & 0xFFFFFFFF
# Compute the Nth prime where N is a fixed constant.
# The loop below uses a growing list of known primes and trial division.
N = 10001 # target ordinal of the prime (one-based)
primes = [2]
candidate = 3
while len(primes) < N:
is_prime = True
# trial division by known primes up to sqrt(candidate)
for p in primes:
if p * p > candidate:
break
if candidate % p == 0:
is_prime = False
break
if is_prime:
primes.append(candidate)
candidate += 2 # skip even numbers
target_prime = primes[N - 1]
# Final check: the input must equal the computed target prime.
return x == target_prime
def mystery(x):
# The input must be a string of exactly 4 characters.
if not isinstance(x, str) or len(x) != 4:
return False
# Convert characters to integer coefficients
coeffs = [ord(c) for c in x]
# Ensure standard printable ASCII to prevent ambiguity
if any(c < 32 or c > 126 for c in coeffs):
return False
# We operate in the finite field GF(257).
# 257 is a Fermat prime (2^8 + 1).
modulus = 257
# The input characters define a polynomial P(z):
# P(z) = coeffs[0] * z^0 + coeffs[1] * z^1 + coeffs[2] * z^2 + coeffs[3] * z^3
# We evaluate this polynomial at four distinct points: z = 1, 2, 3, 4.
targets = [122, 212, 172, 94]
for z in range(1, 5):
val = 0
power_of_z = 1
# Calculate P(z)
for c in coeffs:
val = (val + c * power_of_z) % modulus
power_of_z = (power_of_z * z) % modulus
# Check against the target for this point
if val != targets[z-1]:
return False
return True
def mystery(x):
# Accept only strings (this function hides the real gate among many red herrings).
if not isinstance(x, str):
return False
# Harmless length and printable-character constraints (do not fully determine the solution).
if not (1 <= len(x) <= 64):
return False
for ch in x:
if ord(ch) < 32 or ord(ch) > 126:
return False
# --- Red herrings (intended to distract) ---
# 1) A silly rolling checksum
chk = 0xDEADBEEF
for i, ch in enumerate(x.encode('utf-8')):
chk = ((chk << 3) | (chk >> (64 - 3))) & 0xFFFFFFFFFFFFFFFF
chk ^= (ch + i) & 0xFF
# 2) A fake pseudo-random byte mixing that looks important
data = bytearray(x.encode('utf-8'))
if len(data) == 0:
data = bytearray(b'\x00')
for i in range(len(data)):
j = (i * 31 + 7) % len(data)
data[i], data[j] = (data[i] ^ 0xA5) & 0xFF, (data[j] ^ 0x5A) & 0xFF
# 3) A faux key-derivation loop producing an integer
seed = 1469598103934665603
for b in data:
seed ^= b
seed = (seed * 1099511628211) & 0xFFFFFFFFFFFFFFFF
# --- The real gate (small and precise) ---
# The accepted value is constructed (obfuscated) below.
# The numeric expressions are intentionally nontrivial to read at a glance.
target_bytes = [
(23 * 5) - 2, # 113 -> 'q'
(13 * 9), # 117 -> 'u'
(5 * 20) - 3, # 97 -> 'a'
(5 * 23), # 115 -> 's'
(5 * 20) - 3, # 97 -> 'a'
(19 * 6), # 114 -> 'r'
(4 * 13), # 52 -> '4'
(2 * 25), # 50 -> '2'
(11 * 3), # 33 -> '!'
]
# Build the target string from those byte values.
target = ''.join(chr(b & 0xFF) for b in target_bytes)
# Final decision: only exact match passes.
return x == target