import math
def mystery(x):
"""
This function checks for specific, non-obvious properties
depending on whether the input x is a string or an integer.
"""
def is_prime(n):
"""Helper function to check if a number is prime."""
if n < 2:
return False
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
try:
if isinstance(x, str):
# Condition 1: The string must consist purely of digits.
if not x.isdigit():
return False
num_val = int(x)
# Condition 2: The numerical value of the string must be a perfect square.
if num_val < 0: # Perfect squares are non-negative
return False
sqrt_val = int(math.sqrt(num_val))
if sqrt_val * sqrt_val != num_val:
return False
# Condition 3: The length of the string must be odd.
if len(x) % 2 == 0:
return False
# Condition 4: The string must contain exactly one digit '3'.
if x.count('3') != 1:
return False
# Condition 5: The sum of the ASCII values of all characters in the string
# must be a prime number.
ascii_sum = sum(ord(c) for c in x)
if not is_prime(ascii_sum):
return False
return True # All string conditions met
elif isinstance(x, int):
# Condition 1: The integer must be positive.
if x <= 0:
return False
str_val = str(x)
# Condition 2: The string representation of the integer must not contain the digit '0'.
if '0' in str_val:
return False
# Condition 3: The length of the string representation must be at least 3.
if len(str_val) < 3:
return False
# Condition 4: The integer must be a "Disarium number".
# A Disarium number is a number in which the sum of its digits raised
# to the power of their respective positions is equal to the number itself.
# (Positions are 1-indexed from the left).
sum_of_powers = 0
for i, digit_char in enumerate(str_val):
digit = int(digit_char)
sum_of_powers += digit ** (i + 1) # i is 0-indexed, so i+1 for 1-indexed position
return sum_of_powers == x # All integer conditions met
else:
# If x is neither a string nor an integer, it returns False.
return False
except ValueError:
# Handles cases where int(x) fails for a string (e.g., "abc")
return False
except OverflowError:
# Handles cases with extremely large numbers that cause overflow
return False
except Exception:
# Catch any other unexpected errors
return False
def mystery(x):
"""
Validates a string based on character properties and a
simulated path traversal on a grid.
"""
if not isinstance(x, str):
return False
# 1. Length Check
if len(x) != 6:
return False
# 2. ASCII Sum Check
# The sum of ASCII values of all characters must equal 609.
if sum(ord(c) for c in x) != 609:
return False
# 3. Composition Check
# Must contain exactly two occurrences of the letter 'n'.
if x.count('n') != 2:
return False
# 4. Prefix Check
if not x.startswith('b'):
return False
# 5. Path Simulation
# Simulates movement on a 4x4 grid (indices 0-3).
# The grid cells are numbered 1 to 16 in row-major order.
# Starting position is (0, 0) with initial accumulated value of 1.
r, c = 0, 0
acc = 1
for char in x:
# Movement rule:
# Even ASCII value -> Move Right (column + 1)
# Odd ASCII value -> Move Down (row + 1)
if ord(char) % 2 == 0:
c += 1
else:
r += 1
# Boundary Check: Must stay within 4x4 grid
if r > 3 or c > 3:
return False
# Accumulate the value of the current cell
# Cell value = row * 4 + col + 1
acc += (r * 4 + c + 1)
# 6. Destination Check
# Must end exactly at the bottom-right corner (3, 3).
if (r, c) != (3, 3):
return False
# 7. Path Sum Check
# The sum of values of all visited cells (including start) must be 55.
return acc == 55
import math
def mystery(x):
"""
This function checks for complex properties based on whether the input x
is a string or an integer, involving numerical values of characters,
digit properties, and number classifications.
"""
def is_prime(n):
"""Helper function to check if a number is prime."""
if n < 2:
return False
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
def get_char_numerical_value(char):
"""Helper function to get a=1, b=2, ..., z=26."""
if 'a' <= char <= 'z':
return ord(char) - ord('a') + 1
return -1 # Invalid character
def is_palindrome_number(n):
"""Helper function to check if a number is a palindrome."""
if n < 0: return False
return str(n) == str(n)[::-1]
def is_happy(n):
"""Helper function to check if a number is a Happy Number."""
if n <= 0: return False
seen = set()
current = n
while current != 1 and current not in seen:
seen.add(current)
current = sum(int(digit)**2 for digit in str(current))
return current == 1
def is_perfect_power(n):
"""Helper function to check if a number is a perfect power (m^k for integers m > 1, k > 1)."""
if n <= 1: return False
# Check for powers up to log2(n) for exponent k
for k in range(2, int(math.log2(n)) + 2):
# Calculate m = n^(1/k) and round to nearest integer
m = round(n**(1/k))
# Check if m^k actually equals n
if m**k == n:
return True
return False
try:
if isinstance(x, str):
# Condition 1: The string must consist only of lowercase English letters.
if not x.islower() or not x.isalpha():
return False
# Condition 2: The length of the string must be exactly 5 characters.
if len(x) != 5:
return False
# Condition 3: The string must contain exactly one vowel (a, e, i, o, u).
vowels = "aeiou"
vowel_count = sum(1 for char in x if char in vowels)
if vowel_count != 1:
return False
# Condition 4: The sum of the ASCII values of all characters in the string
# must be a perfect square.
ascii_sum = sum(ord(c) for c in x)
sqrt_sum = int(math.sqrt(ascii_sum))
if sqrt_sum * sqrt_sum != ascii_sum:
return False
# Condition 5: The numerical value of the character at the 3rd position
# (0-indexed, so x[2]) must be a prime number (where a=1, b=2, ..., z=26).
char_val_third_pos = get_char_numerical_value(x[2])
if not is_prime(char_val_third_pos):
return False
return True # All string conditions met
elif isinstance(x, int):
# Condition 1: The integer must be positive.
if x <= 0:
return False
# Condition 2: The integer must be a 4-digit number.
if not (1000 <= x <= 9999):
return False
# Condition 3: The integer must be a "Happy Number".
# A Happy Number is a number that eventually reaches 1 when replaced by the
# sum of the square of each digit.
if not is_happy(x):
return False
# Condition 4: The integer must be a "Perfect Power".
# A Perfect Power is an integer n that can be expressed as m^k
# for integers m > 1 and k > 1.
if not is_perfect_power(x):
return False
# Condition 5: The sum of the digits of the integer must be a "palindrome number".
# A palindrome number reads the same forwards and backwards (e.g., 121, 5, 4334).
sum_digits = sum(int(digit) for digit in str(x))
if not is_palindrome_number(sum_digits):
return False
return True # All integer conditions met
else:
# If x is neither a string nor an integer, it returns False.
return False
except ValueError:
# Handles cases where int(x) fails for a string (e.g., "abc")
return False
except OverflowError:
# Handles cases with extremely large numbers that cause overflow
return False
except Exception:
# Catch any other unexpected errors
return False
def mystery(x):
"""
Validates a 'DNA' sequence based on structural, compositional,
and energetic constraints.
"""
# 1. Type and Length Check
if not isinstance(x, str) or len(x) != 10:
return False
# 2. Alphabet Check
# Must only contain DNA bases (uppercase).
allowed = set('ACGT')
if not set(x).issubset(allowed):
return False
# 3. Pair Balance
# In this hypothetical strand, Adenine (A) must equal Thymine (T),
# and Cytosine (C) must equal Guanine (G).
if x.count('A') != x.count('T') or x.count('C') != x.count('G'):
return False
# 4. Stability Check
# No base can be repeated consecutively (e.g., 'AA' is forbidden).
if any(x[i] == x[i+1] for i in range(len(x) - 1)):
return False
# 5. Motif Check
# The sequence must contain the specific catalytic triad 'CAT'.
if 'CAT' not in x:
return False
# 6. Energetic Resonance
# The sequence's weighted ASCII sum must be a multiple of 13.
# The weight is determined by the character's 1-based position.
# Formula: sum(ASCII_value * (index + 1))
weighted_sum = sum(ord(c) * (i + 1) for i, c in enumerate(x))
return weighted_sum % 13 == 0
import math
def mystery(x):
"""
This function evaluates properties of the input x, taking distinct paths
for strings and integers, focusing on number theory, binary representation,
and hexadecimal string characteristics.
"""
def is_prime(n):
"""Helper function to check if a number is prime."""
if n < 2:
return False
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
def get_prime_factors_sum(n):
"""Helper function to calculate the sum of unique prime factors of n."""
if n <= 1:
return 0
factors_sum = 0
d = 2
temp_n = n
while d * d <= temp_n:
if temp_n % d == 0:
factors_sum += d
while temp_n % d == 0: # Remove all occurrences of this prime factor
temp_n //= d
d += 1
if temp_n > 1: # If temp_n is still > 1, it's the last prime factor
factors_sum += temp_n
return factors_sum
def is_powerful_number(n):
"""
Helper function to check if a number is a "Powerful Number".
A number n is powerful if for every prime factor p of n, p^2 also divides n.
"""
if n <= 0:
return False
if n == 1:
return True # By definition, 1 is a powerful number
temp_n = n
d = 2
while d * d <= temp_n:
if temp_n % d == 0:
# d is a prime factor
# Check if d^2 divides n
if n % (d * d) != 0:
return False
while temp_n % d == 0: # Remove all occurrences of this prime factor
temp_n //= d
d += 1
# If temp_n > 1, it's the last prime factor. We need to ensure that temp_n^2 divides the original n.
if temp_n > 1:
if n % (temp_n * temp_n) != 0:
return False
return True
try:
if isinstance(x, str):
# String path: "Hexadecimal Sequence with Palindromic Properties"
# Condition 1: Must be entirely lowercase hexadecimal digits (0-9, a-f).
if not all(c in '0123456789abcdef' for c in x):
return False
# Condition 2: Length must be a prime number between 5 and 10 (inclusive).
# Possible lengths: 5, 7.
string_length = len(x)
if not (5 <= string_length <= 10 and is_prime(string_length)):
return False
# Condition 3: The string must be a palindrome.
if x != x[::-1]:
return False
# Helper for hexadecimal character to integer conversion
hex_to_int = lambda c: int(c, 16)
# Condition 4: The sum of the numerical values (0-15) of its digits
# must be a prime number.
numerical_sum = sum(hex_to_int(c) for c in x)
if not is_prime(numerical_sum):
return False
# Condition 5: The numerical value of the central character
# (which exists because length is odd) must be a prime number (0-15).
# Primes in 0-15 are: 2, 3, 5, 7, 11, 13.
central_char = x[string_length // 2]
central_val = hex_to_int(central_char)
if not is_prime(central_val):
return False
return True
elif isinstance(x, int):
# Integer path: "Binary-Powerful Number with Digit Constraints"
# Condition 1: Must be a positive integer.
if x <= 0:
return False
# Condition 2: Its binary representation must have a specific length (exactly 10 bits).
# This means x must be in the range [2^9, 2^10 - 1], i.e., [512, 1023].
if not (512 <= x <= 1023):
return False
# Condition 3: The number of '1's in its binary representation must be a prime number.
binary_x = bin(x)[2:] # Remove '0b' prefix
ones_count = binary_x.count('1')
if not is_prime(ones_count): # Primes: 2, 3, 5, 7, ...
return False
# Condition 4: The integer must be a "Powerful Number".
if not is_powerful_number(x):
return False
# Condition 5: The sum of its unique prime factors must be a two-digit prime number.
# (e.g., 11, 13, 17, 19, ..., 97).
unique_prime_factors_sum = get_prime_factors_sum(x)
if not (10 <= unique_prime_factors_sum <= 99 and is_prime(unique_prime_factors_sum)):
return False
return True
else:
# If x is neither a string nor an integer, it returns False.
return False
except ValueError:
# Handles cases like int("abc") or other conversion issues
return False
except OverflowError:
# Handles cases with extremely large numbers
return False
except Exception:
# Catch any other unexpected errors
return False
def mystery(x):
"""
This function validates a string based on structural patterns,
character frequency, and numerical partitions.
"""
if not isinstance(x, str):
return False
# 1. Basic Format Checks
# The string must be exactly 10 lowercase English letters.
if len(x) != 10 or not x.islower() or not x.isalpha():
return False
# 2. Alternating Pattern Constraint
# The string must strictly alternate between vowels and consonants.
# Vowels are defined as 'a', 'e', 'i', 'o', 'u'.
vowels = set('aeiou')
is_prev_vowel = x[0] in vowels
for i in range(1, len(x)):
is_curr_vowel = x[i] in vowels
if is_prev_vowel == is_curr_vowel:
return False
is_prev_vowel = is_curr_vowel
# 3. Frequency Constraint
# No character can appear more than twice in the string.
from collections import Counter
counts = Counter(x)
if any(c > 2 for c in counts.values()):
return False
# 4. Substring Constraint
# The string must contain the substring "key".
if "key" not in x:
return False
# 5. Numerical Partition Constraint
# We map characters to values: a=0, b=1, ..., z=25.
vals = [ord(c) - ord('a') for c in x]
# Condition A: The sum of all values must be exactly 90.
if sum(vals) != 90:
return False
# Condition B: The string is split into two halves (first 5 chars, last 5 chars).
# The product of (value + 1) for the first half must equal
# the product of (value + 1) for the second half.
prod1 = 1
for v in vals[:5]:
prod1 *= (v + 1)
prod2 = 1
for v in vals[5:]:
prod2 *= (v + 1)
if prod1 != prod2:
return False
return True
import math
def mystery(x):
"""
This function evaluates inputs based on various numerical and string properties,
including digit uniqueness, iterative sums, prime factors, and binary patterns.
"""
def is_prime(n):
"""Helper function to check if a number is prime."""
if n < 2:
return False
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
def sum_digits(n):
"""Helper function to calculate the sum of digits of a number."""
return sum(int(d) for d in str(abs(n)))
def is_perfect_square(n):
"""Helper function to check if a number is a perfect square."""
if n < 0:
return False
if n == 0: # 0 is a perfect square (0*0)
return True
sqrt_n = int(math.sqrt(n))
return sqrt_n * sqrt_n == n
def get_sum_of_digits_after_rev_add(n, iterations):
"""
Helper function to perform reverse-and-add iterations
and return the sum of digits of the final number.
"""
current = n
for _ in range(iterations):
rev_current = int(str(current)[::-1])
current += rev_current
return sum_digits(current)
try:
if isinstance(x, str):
# Condition 1: The string must consist purely of 6 digits.
if not x.isdigit() or len(x) != 6:
return False
# Condition 2: All digits in the string must be unique.
if len(set(x)) != 6:
return False
num_val = int(x)
# Condition 3: The sum of digits of the number obtained after 3 "reverse-and-add"
# iterations must be a prime number.
# Example: 196 -> (196+691)=887 -> (887+788)=1675 -> (1675+5761)=7436. Sum digits(7436) = 20.
if not is_prime(get_sum_of_digits_after_rev_add(num_val, 3)):
return False
# Condition 4: The sum of the numerical values of its digits must be a prime number.
if not is_prime(sum_digits(num_val)):
return False
# Condition 5: The product of the numerical values of its digits must be a perfect cube.
product_digits = 1
for digit_char in x:
product_digits *= int(digit_char)
# A number n is a perfect cube if n^(1/3) is an integer. 0 is a perfect cube (0^3).
if product_digits < 0: # Product of digits cannot be negative
return False
cbrt_prod = round(product_digits**(1/3))
if cbrt_prod * cbrt_prod * cbrt_prod != product_digits:
return False
return True # All string conditions met
elif isinstance(x, int):
# Condition 1: The integer must be positive.
if x <= 0:
return False
# Condition 2: The integer must be a 3-digit number.
if not (100 <= x <= 999):
return False
# Condition 3: The integer must be a multiple of 7.
if x % 7 != 0:
return False
# Condition 4: The sum of its digits must be an even number.
if sum_digits(x) % 2 != 0:
return False
# Condition 5: The number of '1's in its binary representation must be exactly 4.
binary_x = bin(x)[2:] # Remove '0b' prefix
if binary_x.count('1') != 4:
return False
return True # All integer conditions met
else:
# If x is neither a string nor an integer, it returns False.
return False
except ValueError:
# Handles cases where int(x) fails for a string (e.g., "abc")
return False
except OverflowError:
# Handles cases with extremely large numbers that cause overflow
return False
except Exception:
# Catch any other unexpected errors
return False
def mystery(x):
"""
Validates a path string for an archaeological expedition simulation.
The string represents a sequence of moves and actions on a 2D grid.
"""
if not isinstance(x, str):
return False
# 1. Character Validation
# Only cardinal directions and 'D' for Dig allowed.
allowed = set('NEWSD')
if not set(x).issubset(allowed):
return False
# 2. Keyword Check
# The expedition string must contain the substring 'END'.
if 'END' not in x:
return False
# 3. Checksum
# The sum of ASCII values of the string must be a multiple of 71.
if sum(ord(c) for c in x) % 71 != 0:
return False
# 4. Path Simulation
# Start at (0,0). Track visited locations to prevent loops
# (except for returning to start at the very end).
x_pos, y_pos = 0, 0
visited = {(0, 0)}
dig_sites = []
moves = {
'N': (0, 1), 'S': (0, -1),
'E': (1, 0), 'W': (-1, 0)
}
for i, char in enumerate(x):
if char == 'D':
# Dig at current location
current_site = (x_pos, y_pos)
dig_sites.append(current_site)
# Cannot dig same spot twice
if dig_sites.count(current_site) > 1:
return False
else:
dx, dy = moves[char]
x_pos += dx
y_pos += dy
new_pos = (x_pos, y_pos)
# Crossing check:
# Can only visit a spot if it's new, OR if it's the
# very last move returning to (0,0).
if new_pos in visited:
is_last_move = (i == len(x) - 1)
if not (is_last_move and new_pos == (0, 0)):
return False
visited.add(new_pos)
# 5. Path Loop Check
# Must end back at (0,0).
if (x_pos, y_pos) != (0, 0):
return False
# 6. Excavation Count
# Must dig exactly 3 times.
if len(dig_sites) != 3:
return False
# 7. Geometry Check
# The three dig sites must form a Right-Angled Triangle.
p1, p2, p3 = dig_sites
# Squared distances between points
d1 = (p1[0]-p2[0])**2 + (p1[1]-p2[1])**2
d2 = (p2[0]-p3[0])**2 + (p2[1]-p3[1])**2
d3 = (p3[0]-p1[0])**2 + (p3[1]-p1[1])**2
sides = sorted([d1, d2, d3])
# Pythagorean theorem: a^2 + b^2 = c^2 (sides are already squared)
if sides[0] + sides[1] != sides[2]:
return False
# 8. Area Check
# The area of the triangle must be exactly 6.
# Shoelace formula for area
xs = [p[0] for p in dig_sites]
ys = [p[1] for p in dig_sites]
lhs = sum(xs[i] * ys[(i+1)%3] for i in range(3))
rhs = sum(xs[(i+1)%3] * ys[i] for i in range(3))
area = abs(lhs - rhs) / 2.0
return area == 6.0
import math
def mystery(x):
"""
This function evaluates inputs based on a unique set of constraints
for strings (character patterns, ASCII properties) and integers
(number theory, binary representation).
"""
def is_prime(n):
"""Helper function to check if a number is prime."""
if n < 2:
return False
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
def sum_digits(n):
"""Helper function to calculate the sum of digits of a number."""
return sum(int(d) for d in str(abs(n)))
def is_perfect_square(n):
"""Helper function to check if a number is a perfect square."""
if n < 0:
return False
if n == 0:
return True
sqrt_n = int(math.sqrt(n))
return sqrt_n * sqrt_n == n
def get_distinct_prime_factors(n):
"""Helper function to get the set of distinct prime factors of n."""
if n <= 1:
return set()
factors = set()
d = 2
temp_n = n
while d * d <= temp_n:
if temp_n % d == 0:
factors.add(d)
while temp_n % d == 0:
temp_n //= d
d += 1
if temp_n > 1:
factors.add(temp_n)
return factors
def get_char_numerical_value(char):
"""Helper function to get a=1, b=2, ..., z=26."""
if 'a' <= char <= 'z':
return ord(char) - ord('a') + 1
return -1 # Invalid character
def is_vowel(char):
"""Helper function to check if a character is a vowel."""
return char in 'aeiou'
try:
if isinstance(x, str):
# String Path: "ASCII Sum & Pattern"
# Condition 1: Length must be exactly 6 characters.
if len(x) != 6:
return False
# Condition 2: All characters must be lowercase English letters.
if not x.islower() or not x.isalpha():
return False
# Condition 3: The string must follow a strict CVCVCV (Consonant-Vowel-Consonant-Vowel-Consonant-Vowel) pattern.
for i, char in enumerate(x):
if i % 2 == 0: # Even index (0, 2, 4) should be a consonant
if is_vowel(char):
return False
else: # Odd index (1, 3, 5) should be a vowel
if not is_vowel(char):
return False
# Condition 4: All characters in the string must be unique.
if len(set(x)) != 6:
return False
# Condition 5: The sum of the ASCII values of all characters must be between 600 and 650 (inclusive).
ascii_sum = sum(ord(c) for c in x)
if not (600 <= ascii_sum <= 650):
return False
# Condition 6: The sum of (numerical_value * (index + 1)) for all characters
# must be a prime number. (a=1, b=2, ..., z=26)
positional_numerical_sum = sum(get_char_numerical_value(c) * (i + 1) for i, c in enumerate(x))
if not is_prime(positional_numerical_sum):
return False
return True
elif isinstance(x, int):
# Integer Path: "Number Property Chain"
# Condition 1: Must be a 5-digit number (10000-99999).
if not (10000 <= x <= 99999):
return False
# Condition 2: The sum of its digits (base 10) must be a perfect square.
digit_sum_base10 = sum_digits(x)
if not is_perfect_square(digit_sum_base10):
return False
# Condition 3: The sum of its distinct prime factors must be a prime number.
distinct_prime_factors = get_distinct_prime_factors(x)
sum_distinct_prime_factors = sum(distinct_prime_factors)
if not is_prime(sum_distinct_prime_factors):
return False
# Condition 4: Its binary representation (without '0b' prefix) must be a palindrome.
binary_x = bin(x)[2:]
if not (binary_x == binary_x[::-1]):
return False
# Condition 5: The count of '1's in its binary representation must be a prime number.
ones_count_binary = binary_x.count('1')
if not is_prime(ones_count_binary):
return False
return True
else:
# If x is neither a string nor an integer, it returns False.
return False
except ValueError:
# Handles cases like int("abc") or other conversion issues
return False
except OverflowError:
# Handles cases with extremely large numbers
return False
except Exception:
# Catch any other unexpected errors
return False
def mystery(x):
"""
Analyzes a string representing a chemical-like formula to validate
its structural, atomic, and numerical properties.
"""
if not isinstance(x, str):
return False
# 1. Format Check
# The string must be exactly 8 characters long.
# It must follow the pattern: Element-Count-Element-Count...
# (4 pairs of an Uppercase Letter followed by a Digit)
if len(x) != 8:
return False
elements = x[0::2] # Indices 0, 2, 4, 6
counts = x[1::2] # Indices 1, 3, 5, 7
if not elements.isalpha() or not elements.isupper():
return False
if not counts.isdigit() or '0' in counts: # Counts must be 1-9
return False
# 2. Structural Constraints
# Must contain exactly 4 distinct elements.
if len(set(elements)) != 4:
return False
# The formula must start with Carbon ('C') and the last element group must be Hydrogen ('H').
if elements[0] != 'C' or elements[-1] != 'H':
return False
# 3. ASCII Resonance
# The sum of the ASCII values of the 4 element symbols must be a perfect square.
ascii_sum = sum(ord(e) for e in elements)
if int(ascii_sum**0.5)**2 != ascii_sum:
return False
# 4. Atomic Mass Calculation
# Uses standard integer atomic weights for a subset of elements.
periodic_table = {
'H': 1, 'C': 12, 'N': 14, 'O': 16,
'F': 19, 'P': 31, 'S': 32, 'K': 39
}
if not all(e in periodic_table for e in elements):
return False
total_weight = 0
total_atoms = 0
for i in range(4):
el = elements[i]
cnt = int(counts[i])
total_weight += periodic_table[el] * cnt
total_atoms += cnt
# 5. Stability Checks
# The calculated molecular weight must be a palindrome number.
s_weight = str(total_weight)
if s_weight != s_weight[::-1]:
return False
# The total number of atoms in the molecule must be a prime number.
def is_prime(n):
if n < 2: return False
for i in range(2, int(n**0.5) + 1):
if n % i == 0: return False
return True
if not is_prime(total_atoms):
return False
# 6. Quantum Link
# The total atom count must be exactly 8 more than the sum of the digits of the molecular weight.
weight_digit_sum = sum(int(d) for d in s_weight)
return total_atoms == weight_digit_sum + 8