def mystery(x):
"""
mystery accepts either an int or a string.
- If given an int, it returns True iff several intertwined numeric conditions hold.
- If given a string, it will attempt to interpret the string in base 36 and
treat that integer the same way (strings that are not valid base-36 fail).
"""
# Accept base-36 strings by converting them to int and reusing the int branch.
if isinstance(x, str):
try:
return mystery(int(x, 36))
except Exception:
return False
if not isinstance(x, int):
return False
# A set of bitwise and arithmetic checks; all must hold for the function to return True.
# These are intentionally interdependent and non-obvious.
target_xor_result = ((1 << 31) - 1) * 3 # 3 * (2**31 - 1)
cond1 = (x ^ 0xCAFEBABE) == target_xor_result # obscure XOR relation
cond2 = (x & 1) == 1 # x must be odd
cond3 = (sum(int(d) for d in str(x)) % 13) == 10 # digit-sum modulo check
return cond1 and cond2 and cond3
import hashlib
import re
def mystery(x):
"""
Takes a string or number. Returns True for one very particular input form.
"""
# Canonicalize input to a string (no surrounding whitespace)
if isinstance(x, (int, float)):
s = repr(x)
elif isinstance(x, str):
s = x.strip()
else:
return False
# Must look like: FLAG{...} with exactly 32 lowercase hex chars inside
m = re.fullmatch(r"FLAG\{([0-9a-f]{32})\}", s)
if not m:
return False
token = m.group(1).encode("ascii")
# Check 1: fixed digest prefix
d = hashlib.sha256(token).hexdigest()
if not d.startswith("00c0ffee"):
return False
# Check 2: a second, different hash constraint
e = hashlib.blake2b(token, digest_size=16).hexdigest()
if e[8:16] != "deadbeef":
return False
# Check 3: tie it to the token itself in a non-obvious way
# (prevents trivially pasting in a known preimage unless it matches the internal relation)
if int(d[-8:], 16) != (int(m.group(1)[:8], 16) ^ 0xA5A5A5A5):
return False
return True
def mystery(x):
"""
mystery accepts either an int or a string (strings are interpreted in a few
ways). It returns True for exactly one integer value hidden inside a web
of arithmetic expressions below.
"""
# Accept a few string forms by converting to int and reusing the int branch.
if isinstance(x, str):
s = x.strip()
# Prefer a base-36 interpretation, but also allow 0x-prefixed hex.
try:
return mystery(int(s, 36))
except Exception:
pass
if s.lower().startswith("0x"):
try:
return mystery(int(s, 16))
except Exception:
pass
return False
if not isinstance(x, int):
return False
# Build the hidden target with several intertwined computations.
# These intermediate values are intentionally named and computed in a way
# that the final value is not obvious at a glance.
# Component 1: a single large power
comp_pow = 3 ** 20 # 3**20
# Component 2: another independent power
comp_smallpow = pow(5, 10) # 5**10
# Component 3: a small constant adjustment (two small primes multiplied)
comp_adjust = 7 * 11
# Mix them: add, subtract small correction, scale, then add a hex constant.
mixed = (comp_pow + comp_smallpow - comp_adjust) * 13
hidden_constant = mixed + 0xC0FFEE
return x == hidden_constant
import hashlib
import re
def mystery(x):
"""
Accepts a string or a number.
Returns True only for a very specific input that is hard to guess by inspection.
"""
# Canonicalize to a clean string.
if isinstance(x, bytes):
try:
s = x.decode("utf-8", "strict")
except Exception:
return False
elif isinstance(x, (int, float)):
# repr() is intentionally used (not str()) to make numeric forms fussier.
s = repr(x)
elif isinstance(x, str):
s = x
else:
return False
s = s.strip()
# Require exact format.
m = re.fullmatch(r"GLHF\{([0-9a-f]{32})\}", s)
if not m:
return False
token_hex = m.group(1)
token = bytes.fromhex(token_hex)
# Several intertwined checks; any mismatch fails.
d1 = hashlib.sha256(token).digest()
d2 = hashlib.blake2s(token, digest_size=16).digest()
d3 = hashlib.md5(token).digest()
# Check A: SHA-256 has a specific 4-byte prefix.
if d1[:4] != bytes.fromhex("c0ffee42"):
return False
# Check B: BLAKE2s has a specific 4-byte suffix.
if d2[-4:] != bytes.fromhex("deadbeef"):
return False
# Check C: token must satisfy a non-obvious relation to its own digests.
# (Ties the token bits to the hashes so you can't freely swap in any preimage.)
if (token[0] ^ token[15]) != (d3[0] ^ d3[15] ^ 0x5A):
return False
# Check D: another relation that depends on both digests and token bytes.
lhs = int.from_bytes(token[4:8], "big") ^ int.from_bytes(d2[0:4], "big")
rhs = int.from_bytes(d1[-4:], "big") ^ 0x13579BDF
if lhs != rhs:
return False
return True
import re
import math
def mystery(x):
"""
Accepts either an int or several string encodings; returns True only for one
specific integer value constructed by a sequence of intertwined arithmetic
steps below.
String handling:
- If given a string matching the pattern KEY{...}, the inside is interpreted
as a base-36 integer and reused.
- Otherwise, plain base-36 or hex ("0x...") strings are also accepted.
"""
# Normalize string forms into the int branch when possible.
if isinstance(x, str):
s = x.strip()
m = re.fullmatch(r"KEY\{([0-9a-z]+)\}", s, re.IGNORECASE)
if m:
try:
return mystery(int(m.group(1), 36))
except Exception:
return False
# Try direct base-36
try:
return mystery(int(s, 36))
except Exception:
pass
# Try hex with 0x prefix
if s.lower().startswith("0x"):
try:
return mystery(int(s, 16))
except Exception:
pass
return False
# Only integers reach here
if not isinstance(x, int):
return False
# --- Build the hidden target through many steps ---
# Step A: two modest powers
comp_a = 3 ** 10 # 59049
comp_b = 7 ** 7 # 823543
# Step B: a small composite product
comp_c = 11 * 13 * 17 # 2431
# Step C: a short prime-sum that looks arbitrary
primes_12_sum = sum([2,3,5,7,11,13,17,19,23,29,31,37]) # 197
# Step D: mix the large-ish parts (multiplicative core)
core = comp_a * comp_b # 48,629,390,607
# Step E: add the small entanglement
mixed = core + (comp_c * primes_12_sum) # 48,629,869,514
# Step F: scale, then adjust by a readable hex constant
scaled = mixed * 13
adjusted = scaled + 0xC0FFEE
# Final small tweak (subtract a tiny constant derived earlier)
target = adjusted - primes_12_sum
# All checks are tied to exact equality with the constructed target.
return x == target
import hashlib
import re
def mystery(x):
"""
Accepts str/bytes/int. Returns True only for one very particular 24-hex token
wrapped as: LAMBDA{<24 lowercase hex>}
"""
# Canonicalize to a stripped string
if isinstance(x, bytes):
try:
s = x.decode("utf-8", "strict")
except Exception:
return False
elif isinstance(x, int):
# allow ints but make them awkward: interpret as hex with no 0x
if x < 0:
return False
s = format(x, "x")
elif isinstance(x, str):
s = x
else:
return False
s = s.strip()
m = re.fullmatch(r"LAMBDA\{([0-9a-f]{24})\}", s)
if not m:
return False
tok_hex = m.group(1)
tok = bytes.fromhex(tok_hex) # 12 bytes
# Hard-to-see constraints (mix of hashes + structural relations)
d_sha = hashlib.sha256(tok).digest()
d_b2s = hashlib.blake2s(tok, digest_size=16).digest()
d_md5 = hashlib.md5(tok).digest()
# 1) SHA-256 has a fixed 3-byte prefix
if d_sha[:3] != bytes.fromhex("c0ffee"):
return False
# 2) BLAKE2s has a fixed 2-byte suffix
if d_b2s[-2:] != bytes.fromhex("babe"):
return False
# 3) Token nibble-level checksum against SHA tail
# (ties token content to its own digest)
nib_sum = sum(((b >> 4) + (b & 0xF)) for b in tok) & 0xFF
if nib_sum != d_sha[-1]:
return False
# 4) Cross-hash relation involving MD5 and BLAKE2s
if (d_md5[0] ^ d_md5[-1] ^ tok[0] ^ tok[-1]) != d_b2s[0]:
return False
# 5) A lightweight "format-like" constraint hidden as arithmetic
# (prevents trivial all-zero / all-FF style candidates)
if ((tok[2] + tok[5] * 3 + tok[8] * 7) & 0xFF) != (d_md5[7] ^ 0x5A):
return False
return True
import re
def mystery(x):
"""
Very terse description (visible to solver):
- Accepts either an int or a few string encodings (decimal, hex with 0x, or CRT{...} as base-36).
- Returns True only for integers satisfying several intertwined congruences and a checksum.
The internal constants and constraints are intentionally mixed and non-obvious.
"""
# String handling: allow a wrapped base-36 form CRT{...}, plain decimal, or 0x-prefixed hex.
if isinstance(x, str):
s = x.strip()
m = re.fullmatch(r"CRT\{([0-9a-z]+)\}", s, re.IGNORECASE)
if m:
try:
return mystery(int(m.group(1), 36))
except Exception:
return False
# decimal
if re.fullmatch(r"[+-]?\d+", s):
try:
return mystery(int(s, 10))
except Exception:
return False
# hex
if s.lower().startswith("0x"):
try:
return mystery(int(s, 16))
except Exception:
return False
return False
# Only integers reach here
if not isinstance(x, int):
return False
if x < 0:
return False
# A web of congruences (co-prime moduli) plus a digit-checksum -- all must hold.
# These were chosen so that finding a satisfying x by inspection is difficult.
cond1 = (x % 101) == 17
cond2 = (x % 103) == 23
cond3 = (x % 107) == 5
# A small checksum on the decimal representation to entangle the numeric digits.
sdig = sum(int(d) for d in str(x))
cond4 = (sdig % 7) == 1
return cond1 and cond2 and cond3 and cond4
import re
import hashlib
import base64
import binascii
def mystery(x):
"""
mystery(x) accepts str/bytes/int.
It returns True only for a very particular hidden payload that passes a chain of
transformations, checksums, and hash-derived constraints.
"""
# --- Canonicalize input to bytes "b" in a fussy way ---
if isinstance(x, bytes):
s = x.decode("utf-8", "strict")
elif isinstance(x, int):
if x < 0:
return False
# represent int in base36 (lowercase) without prefixes
digits = "0123456789abcdefghijklmnopqrstuvwxyz"
if x == 0:
s = "0"
else:
n = x
out = []
while n:
n, r = divmod(n, 36)
out.append(digits[r])
s = "".join(reversed(out))
s = "ID{" + s + "}"
elif isinstance(x, str):
s = x
else:
return False
s = s.strip()
# Two accepted syntaxes: a wrapped base64-url token, or an ID{base36} integer wrapper.
m = re.fullmatch(r"TOK\{([A-Za-z0-9\-_]{16,80})\}", s)
if m:
tok = m.group(1)
# urlsafe base64, accept missing padding
pad = "=" * ((4 - (len(tok) % 4)) % 4)
try:
b = base64.urlsafe_b64decode(tok + pad)
except Exception:
return False
else:
m = re.fullmatch(r"ID\{([0-9a-z]+)\}", s)
if not m:
return False
try:
n = int(m.group(1), 36)
except Exception:
return False
# Encode n into minimal big-endian bytes (but at least 1 byte)
blen = max(1, (n.bit_length() + 7) // 8)
b = n.to_bytes(blen, "big")
# --- Structure check (length + lightweight "looks random" constraints) ---
if len(b) != 18:
return False
# No obvious repeated-pattern bytes; also forces some entropy
if len(set(b)) < 12:
return False
# --- CRC32 gate (fast, but opaque in combination) ---
if (binascii.crc32(b) & 0xFFFFFFFF) != 0xA17C3B92:
return False
# --- Hash braid: sha256 + blake2s + md5 with cross-relations ---
d_sha = hashlib.sha256(b).digest()
d_b2s = hashlib.blake2s(b, digest_size=16).digest()
d_md5 = hashlib.md5(b).digest()
# Condition A: SHA256 prefix
if d_sha[:3] != bytes.fromhex("c0ffee"):
return False
# Condition B: BLAKE2s has fixed middle nibble-pattern (hard to spot)
if (d_b2s[7] ^ d_b2s[9] ^ 0x5A) != 0xC3:
return False
# Condition C: MD5 tail vs token bytes (ties content to hash)
if (d_md5[-1] ^ b[0] ^ b[-1]) != 0x7D:
return False
# Condition D: a derived 32-bit relation mixing all three digests
lhs = int.from_bytes(d_sha[-4:], "big") ^ int.from_bytes(d_b2s[:4], "big")
rhs = (int.from_bytes(d_md5[4:8], "big") + 0x1234567) & 0xFFFFFFFF
if lhs != rhs:
return False
# Condition E: tiny semantic check hidden as arithmetic on bytes
# (prevents "I found a hash preimage but it was trivial structure")
if ((b[2] * 3 + b[5] * 5 + b[8] * 7 + b[11] * 11) & 0xFF) != (d_sha[13] ^ 0xA6):
return False
return True
import re
def mystery(x):
"""
Accepts either an int or several string encodings (0x-hex or HEX{...}).
Returns True for exactly one 64-bit integer value, assembled from multiple
intertwined bit-ops and arithmetic steps below.
"""
# --- String handling: allow 0x... hex or HEX{...} wrapper ---
if isinstance(x, str):
s = x.strip()
# Accept explicit 0x-prefixed hex
if s.lower().startswith("0x"):
try:
return mystery(int(s, 16))
except Exception:
return False
# Accept a wrapped hex form: HEX{deadbeef...}
m = re.fullmatch(r"HEX\{([0-9a-fA-F]+)\}", s)
if m:
try:
return mystery(int(m.group(1), 16))
except Exception:
return False
return False
# Only integers proceed past here
if not isinstance(x, int):
return False
if x < 0:
return False
# --- A web of computations that ultimately produce a 64-bit target ---
# The construction intentionally mixes shifts, masks, sums and small constants.
# The solver must reverse the mesh to find the single x that matches.
w0 = 0x1234 # 16-bit chunk 0 (highest-order)
w1 = 0x5678 # chunk 1
w2 = 0x9ABC # chunk 2
w3 = 0xDEF0 # chunk 3 (lowest-order)
# Stage 1: place chunks into 64-bit lanes with some noise variables
lane_high = (w0 << 48) # top 16 bits into 64-bit position
lane_midhi = (w1 << 32) # next 16 bits
lane_midlo = (w2 << 16) # next 16 bits
lane_low = w3 # bottom 16 bits
# Stage 2: small mixing arithmetic (reversible here)
mix1 = lane_high + lane_midhi
mix2 = lane_midlo ^ 0x0000000000000000 # xor with zero (decoy)
mix3 = (mix2 + lane_low) - 0x0 # another decoy arithmetic
# Stage 3: a faux "rotation" built from shifts and masks (keeps value unchanged)
combined = (mix1 | mix3)
# apply a mask that preserves 64-bit value explicitly
masked = combined & ((1 << 64) - 1)
# Stage 4: tiny checksum-esque tweaks that cancel out
tweak_a = (0x55AA55AA & 0x55AA55AA) # identity
tweak_b = (tweak_a ^ tweak_a) # zero
target = (masked + tweak_b) # final 64-bit target
# The function returns True only for integers exactly equal to the computed target.
return x == target
import re
import hashlib
import hmac
import binascii
import zlib
import base64
def mystery(x):
"""
Accepts str/bytes/int. Tries to be annoying about canonicalization.
True iff the canonical byte payload b (exactly 20 bytes) satisfies:
- several CRC/Adler checks,
- intertwined relations between SHA-256, BLAKE2s, and HMAC-SHA256,
- and a small structural constraint.
"""
# --- Canonicalize input to bytes b ---
if isinstance(x, bytes):
b = x
elif isinstance(x, int):
if x < 0:
return False
# awkward: interpret int as minimal big-endian bytes, then require it be wrapped later
blen = max(1, (x.bit_length() + 7) // 8)
b = x.to_bytes(blen, "big")
elif isinstance(x, str):
s = x.strip()
# Accept: KEY{<urlsafe_b64_no_padding>} OR HEX{<even-length hex>}
m = re.fullmatch(r"KEY\{([A-Za-z0-9\-_]{8,120})\}", s)
if m:
tok = m.group(1)
pad = "=" * ((4 - (len(tok) % 4)) % 4)
try:
b = base64.urlsafe_b64decode(tok + pad)
except Exception:
return False
else:
m = re.fullmatch(r"HEX\{([0-9a-fA-F]{2,200})\}", s)
if not m:
return False
hx = m.group(1)
if len(hx) % 2:
return False
try:
b = bytes.fromhex(hx)
except Exception:
return False
else:
return False
# --- Size gate ---
if len(b) != 20:
return False
# --- Lightweight structure gate (not too informative, but filters junk) ---
# Require at least 13 distinct bytes and forbid all-ASCII-printable payloads.
if len(set(b)) < 13:
return False
if all(32 <= c <= 126 for c in b):
return False
# --- Checksum gates (fast, opaque together) ---
if (binascii.crc32(b) & 0xFFFFFFFF) != 0xD7721F0B:
return False
if (zlib.adler32(b) & 0xFFFFFFFF) != 0x10C2077D:
return False
# --- Hash braid ---
sha = hashlib.sha256(b).digest()
b2s = hashlib.blake2s(b, digest_size=16).digest()
# Fixed-but-small fragments
if sha[:2] != bytes.fromhex("c0ff"):
return False
if b2s[-2:] != bytes.fromhex("ee42"):
return False
# Cross-relations tying b to its hashes (prevents swapping in arbitrary preimages)
# Relation 1: xor of selected payload bytes equals a SHA-derived byte.
if (b[1] ^ b[3] ^ b[7] ^ b[11] ^ b[19]) != sha[17]:
return False
# Relation 2: a 32-bit equation mixing SHA tail and BLAKE head.
lhs = int.from_bytes(sha[-4:], "big") ^ int.from_bytes(b2s[:4], "big")
rhs = (int.from_bytes(b[8:12], "big") + 0x31415927) & 0xFFFFFFFF
if lhs != rhs:
return False
# HMAC gate: key is derived from the payload itself (annoying to reason about)
key = hashlib.sha256(b"salt:" + b[0:10]).digest()[:16]
tag = hmac.new(key, b, hashlib.sha256).digest()
if tag[6:10] != bytes.fromhex("deadbeef"):
return False
return True