def mystery(x):
s = str(x).strip()
if s[:1] in "+-" or not s.isdecimal() or len(s) != 4:
return False
n = int(s)
mods = [0b111, 0b1011, 0b1101, 0b10001]
rems = [0b101, 0b100, 0b110, 0b1001]
return all(n % m == r for m, r in zip(mods, rems))
def mystery(x):
s = str(x).strip()
if not s.isdigit() or len(s) != 5:
return False
n = int(s)
mods = [0b10001, 0b10111, 0b11101, 0b11111]
rems = [0b11, 0b10001, 0b10100, 0b111]
return all(n % m == r for m, r in zip(mods, rems))
def mystery(x):
s = str(x)
if len(s) != 6 or not all('a' <= c <= 'z' for c in s):
return False
idx = [ord(c) - 97 for c in s]
if sum(idx) != 97:
return False
idx = [idx[4], idx[1], idx[5], idx[0], idx[2], idx[3]]
idx = [(25 - v + i * i) % 26 for i, v in enumerate(idx)]
return ''.join(chr(v + 97) for v in idx) == "ggesph"
def mystery(x):
s = str(x).strip()
if not s.isdigit() or len(s) != 6:
return False
n = int(s)
mods = [0b100101, 0b101001, 0b101011, 0b101111, 0b110101]
rems = [0b11000, 0b101, 0b11, 0b100010, 0b10011]
return all(n % m == r for m, r in zip(mods, rems))
def mystery(x):
s = str(x).strip()
if len(s) != 8 or any(c < 'a' or c > 'z' for c in s):
return False
v = [ord(c) - 97 for c in s]
if (sum(v) + 0b111 * v[2] + 0b1011 * v[5]) % 0b11010 != 0b10001:
return False
v = [v[6], v[1], v[4], v[7], v[0], v[5], v[2], v[3]]
m = [0b101, 0b111, 0b1001, 0b1011, 0b1101, 0b1111, 0b10001, 0b10011]
a = [0b1, 0b11, 0b101, 0b111, 0b1001, 0b1011, 0b1101, 0b1111]
v = [(v[i] * m[i] + a[i]) % 26 for i in range(8)]
for i in range(1, 8):
v[i] = (v[i] + 3 * v[i - 1] + i * i) % 26
return v == [0b1, 0b10010, 0b1100, 0b10011, 0b10001, 0b1, 0b100, 0b1001]
def mystery(x):
s = str(x).strip()
if len(s) != 7 or not all('a' <= c <= 'z' for c in s):
return False
v = [ord(c) - 97 for c in s]
if sum(v) != 0b1010111:
return False
v = [v[3], v[0], v[6], v[2], v[5], v[4], v[1]]
m = [0b11, 0b101, 0b111, 0b1001, 0b1011, 0b1101, 0b1111]
a = [0b1, 0b10, 0b100, 0b101, 0b110, 0b111, 0b1000]
v = [(v[i] * m[i] + a[i]) % 26 for i in range(7)]
for i in range(1, 7):
v[i] = (v[i] + 0b11 * v[i - 1] + i * i) % 26
return v == [0b10100, 0b10101, 0b111, 0b10001, 0b101, 0b1000, 0b1011]
def mystery(x):
s = str(x).strip()
if len(s) != 9 or s[0] == "0" or not s.isdigit():
return False
d = [ord(c) - 48 for c in s]
# First gate: a weighted checksum on the original digits.
if (sum(d) + 0b11 * d[2] + 0b101 * d[5] + 0b111 * d[8]) % 0b1011 != 0b100:
return False
# Second gate: another checksum to make the search space less friendly.
if sum((i + 1) * v for i, v in enumerate(d)) % 0b100101 != 0b11100:
return False
# Permutation, then an affine scramble mod 10.
d = [d[0b111], d[0], d[0b100], d[0b1000], d[0b10], d[0b101], d[0b1], d[0b110], d[0b11]]
m = [0b11, 0b111, 0b1001, 0b1, 0b11, 0b111, 0b1001, 0b1, 0b11]
a = [0b1, 0b100, 0b10, 0b1000, 0b101, 0b111, 0b0, 0b110, 0b1001]
d = [(d[i] * m[i] + a[i]) % 10 for i in range(9)]
# Feedback pass: each digit depends on the previous transformed digit.
for i in range(1, 9):
d[i] = (d[i] + 2 * d[i - 1] + i) % 10
return d == [0b111, 0b111, 0b11, 0b11, 0b100, 0b110, 0b1, 0b110, 0b110]
def mystery(x):
s = str(x).strip()
if len(s) != 8 or not all('a' <= c <= 'z' for c in s):
return False
v = [ord(c) - 97 for c in s]
if sum(v) != 0b1111011:
return False
v = [v[0b11], v[0b111], v[0b1], v[0b101], v[0b0], v[0b100], v[0b110], v[0b10]]
m = [0b11, 0b101, 0b111, 0b1011, 0b1101, 0b10001, 0b10011, 0b10111]
a = [0b1, 0b10, 0b100, 0b101, 0b110, 0b111, 0b1000, 0b1001]
v = [(v[i] * m[i] + a[i]) % 26 for i in range(8)]
for i in range(1, 8):
v[i] = (v[i] + 0b101 * v[i - 1] + i * i) % 26
return v == [0b11000, 0b10111, 0b11, 0b1101, 0b10110, 0b10001, 0b1100, 0b10001]
def mystery(x):
s = str(x).strip().lower()
if len(s) != 8 or any(c < 'a' or c > 'z' for c in s):
return False
v = [ord(c) - 97 for c in s]
if (sum(v) + 0b101 * v[2] + 0b1001 * v[5] + 0b1101 * v[7]) % 0b100101 != 0b110:
return False
if (v[0] + (v[1] << 1) + (v[3] << 2) + (v[4] << 3) + (v[6] << 4)) % 0b101001 != 0b101:
return False
v = [v[5], v[0], v[7], v[2], v[6], v[1], v[4], v[3]]
m = [0b11, 0b101, 0b111, 0b1001, 0b1011, 0b1111, 0b10001, 0b10011]
a = [0b1, 0b10, 0b11, 0b100, 0b101, 0b110, 0b111, 0b1000]
v = [(v[i] * m[i] + a[i]) % 26 for i in range(8)]
v = [((v[i] * v[i]) + ((i << 1) | 1)) % 26 for i in range(8)]
for i in range(1, 8):
v[i] = (v[i] + 3 * v[i - 1] + i * i) % 26
return v == [0b1101, 0b10101, 0b10101, 0b1110, 0b11, 0b10110, 0b10, 0b1000]
def mystery(x):
s = str(x).strip().lower()
if len(s) != 9 or any(c < 'a' or c > 'z' for c in s):
return False
v = [ord(c) - 97 for c in s]
if sum(v) != 0b1111101:
return False
if sum(i * vv for i, vv in enumerate(v)) % 0b100101 != 0b100010:
return False
v = [v[0b10], v[0b0], v[0b110], v[0b1], v[0b1000], v[0b101], v[0b11], v[0b111], v[0b100]]
m = [0b11, 0b101, 0b111, 0b10, 0b1011, 0b1101, 0b1, 0b100, 0b110]
a = [0b1, 0b10, 0b11, 0b100, 0b101, 0b110, 0b111, 0b1000, 0b1001]
v = [(v[i] * m[i] + a[i]) % 26 for i in range(9)]
for i in range(1, 9):
v[i] = (v[i] + 0b100 * v[i - 1] + i * i) % 26
return v == [0b11, 0b1100, 0b10010, 0b111, 0b1101, 0b101, 0b11, 0b11, 0b1001]