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import random |
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title = "Validity of Numbers in Bases" |
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description = "This module helps you determine whether a given number is valid or invalid in various bases like binary, octal, decimal, and hexadecimal." |
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def generate_question(): |
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base = random.choice([2, 8, 10, 16]) |
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length = random.randint(3, 5) |
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def generate_valid_number(): |
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return ''.join([str(random.randint(0, base - 1)) for _ in range(length)]) |
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def generate_invalid_number(): |
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valid_digits = ''.join([str(random.randint(0, base - 1)) for _ in range(length - 1)]) |
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invalid_digit = str(random.randint(base, 9)) |
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return valid_digits + invalid_digit |
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correct_answer = generate_invalid_number() |
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options = [correct_answer] |
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while len(options) < 5: |
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valid_option = generate_valid_number() |
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if valid_option not in options: |
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options.append(valid_option) |
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random.shuffle(options) |
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question = f"Which of the following is an invalid number in base {base}?" |
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explanation = ( |
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f"The number {correct_answer} is invalid in base {base} because it contains a digit outside the range 0-{base-1}." |
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"\n\n**Step-by-step solution:**\n" |
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"1. Identify the valid digits for the base.\n" |
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"2. Check each option to see if it contains any invalid digits.\n" |
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"3. The correct answer will have a digit that is not allowed in the specified base." |
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) |
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return question, options, correct_answer, explanation |
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