You are a highly experienced educational content creator  for Indian competitive exams such as Railway (Typist - Non_Technical_Posts) under the subject of Mathematics. The topic is **Number System**.. Your task is to generate a detailed **bilingual explanation (English + Hindi)** for a **mnemonic anagram letter** for topic Number System, using the following inputs.

    Generate a Markdown output using this structure:

    ---

    🧠 **Anagram (Short)**: DIVERSES  
    📖 **Expanded (English)**: Diverse Important Various Essential Rational Subtopics Encompassing Simple Elements  
    📖 **Expanded (Hindi)**: विविध महत्वपूर्ण विभिन्न आवश्यक तार्किक उपविषय सरल तत्वों को समेटे हुए

    ---

    ### 🔠 Letter: D / डि — *Divisibility Rules / विभाज्यता नियम*

    #### 📚 Concept:
    - EN: Divisibility Rules  
    - HI: विभाज्यता नियम

    #### 🧠 Type:
    - EN: Divisibility Rules  
    - HI: विभाज्यता नियम

    #### 📖 Description:
    - EN: Problems related to divisibility by numbers and applying divisibility tests quickly.  
    - HI: संख्याओं द्वारा विभाज्यता और तेज़ विभाज्यता नियमों पर आधारित समस्याएं।

    #### 📌 Explanation:
    - EN: Divisibility rules help quickly check if a number is divisible by another without performing full division. This speeds problem solving in exams.  
    - HI: विभाज्यता नियम बिना पूरी भाग देने के यह जांचने में मदद करते हैं कि कोई संख्या किसी दूसरी संख्या से विभाजित है या नहीं। यह परीक्षा में समस्या समाधान को तेज करता है।

    #### ➗ Formula or Relation:
    - EN: **Number divisible by n if remainder on division by n is 0.**  
    - HI: **संख्या n से विभाजित है यदि n से भाग देने पर शेषफल 0 हो।**

    #### 💡 Example Questions:
    **ENGLISH:**
    ['A factory produces 1,200 items daily. A quality inspector wants to check items that are divisible by both 3 and 5 to identify defective batches. Using divisibility rules, determine how many such items are there in a batch of 1,200. Also, if the inspector samples every 10th item, how many defective items would be assessed in a day?', 'A company’s invoice numbers follow a pattern where all numbers divisible by 6 or 9 are flagged for review. From invoices numbered 1 to 500, how many invoices are flagged? Use divisibility rules to calculate without listing all numbers.', 'During a coding test, candidates must solve problems divisible by 2, 3, or 5 within 1 hour. If there are 100 questions, how many are divisible by 2 or 3 or 5? Use divisibility tests to find the count efficiently.']

    **HINDI:**
    ['एक कारखाना प्रतिदिन 1,200 आइटम बनाता है। एक गुणवत्ता निरीक्षक उन आइटमों को जांचना चाहता है जो 3 और 5 दोनों से विभाजित हो सकते हैं ताकि दोषपूर्ण बैच की पहचान की जा सके। विभाज्यता नियमों का उपयोग करते हुए, पता करें कि 1,200 में से कितने आइटम ऐसे हैं। यदि निरीक्षक हर 10वें आइटम का नमूना लेते हैं, तो प्रतिदिन कितने दोषपूर्ण आइटम जाँचे जाएंगे?', 'कंपनी के चालान नंबरों में पैटर्न है जहाँ सभी ऐसे नंबर जो 6 या 9 से विभाजित हो सकते हैं, जांच के लिए झंडा लगाए जाते हैं। 1 से 500 तक के चालान नंबरों में कितने चालान झंडा लगाए जाएंगे? पूरी संख्या गिने बिना विभाज्यता नियमों का उपयोग करें।', 'कोडिंग टेस्ट के दौरान, उम्मीदवारों को 1 घंटे में 2, 3 या 5 से विभाजित प्रश्न हल करने होते हैं। यदि कुल 100 प्रश्न हैं, तो कितने प्रश्न 2 या 3 या 5 से विभाजित हैं? विभाज्यता नियमों का उपयोग कर प्रभावी तरीके से संख्या पता करें।']

    ---
    object should have:
        - "mnemonic_letter_english", "mnemonic_letter_hindi"
        - "type_english", "type_hindi"
        - "description_english", "description_hindi"
        - "difficulty_level_english", "difficulty_level_hindi"
        - "exam_frequency_english", "exam_frequency_hindi"
        - "time_to_solve_english", "time_to_solve_hindi"
        - "clue_words_english": list of 4-5 identifying keywords/phrases
        - "clue_words_hindi": same in Hindi
        - "what_to_use_english", "what_to_use_hindi"
        - "formula_english", "formula_hindi"
        - "alternative_formulas_english", "alternative_formulas_hindi": list of 2-3 alternative formulas
        - "algorithm_english", "algorithm_hindi": step-by-step string list
        - "quick_method_english", "quick_method_hindi"

        - "example": answer all  the question give as Example Questions.
 
          - Require multi-step calculation or reasoning.
          - NOT be short phrases, fragments, or simplified school-level word problems.each Example Questions should be including:
            - "example_no"
            - "question_english", "question_hindi"
            - "solution_steps_english": step list
            - "solution_steps_hindi": step list
            - "answer_english", "answer_hindi"
            - "verification_english", "verification_hindi"

        - "variations_english", "variations_hindi": list of variation types
        - "related_concepts_english", "related_concepts_hindi": related subtopics or concepts
        - "common_mistakes_english", "common_mistakes_hindi": list of 10 traps or errors
        - "tip_english", "tip_hindi": short-cut or important tip
        - "prerequisite_knowledge_english", "prerequisite_knowledge_hindi": list of 3 concepts
        - "practice_problems_english", "practice_problems_hindi": list of 3  full-length and detailed practical, compact competitive-level example questions** per type.  
      ⚠️ NOTE : Ensure answer all the question of Example Questions in the example key

        Use simple, learner-friendly language and return only the JSON object in your response, formatted with proper indentation and structure.
        Use clear language suitable for aptitude learners and format the JSON cleanly

### 🔁 output JSon should be

```json
            { 
              "mnemonic_letter_english": "",
              "mnemonic_letter_hindi": "",
              "type_english": "",
              "type_hindi": "",
              "description_english": "",
              "description_hindi": "",
              "difficulty_level_english": "",
              "difficulty_level_hindi": "",
              "exam_frequency_english": "",
              "exam_frequency_hindi": "",
              "time_to_solve_english": "",
              "time_to_solve_hindi": "",
              "clue_words_english": [
                  "",
                  "",
                  "",
                  "",
                  ""
              ],
              "clue_words_hindi": [
                  "",
                  "",
                  "",
                  "",
                  ""
              ],
              "what_to_use_english": "",
              "what_to_use_hindi": "",
              "formula_english": "",
              "formula_hindi": "",
              "alternative_formulas_english": [
                  "",
                  ""
              ],
              "alternative_formulas_hindi": [
                  "",
                  ""
              ],
              "algorithm_english": [
                  "",
                  "",
                  "",
                  ""
              ],
              "algorithm_hindi": [
                  "",
                  "",
                  "",
                  ""
              ],
              "quick_method_english": "",
              "quick_method_hindi": "",
              "example": [
                  {
                  "example_no":"",
                  "question_english": "",
                  "question_hindi": "",
                  "solution_steps_english": [
                      "",
                      "",
                      "",
                      "",
                      ""
                  ],
                  "solution_steps_hindi": [
                      "",
                      "",
                      "",
                      "",
                      ""
                  ],
                  "answer_english": "",
                  "answer_hindi": "",
                  "verification_english": "",
                  "verification_hindi": ""
              }..,],
              "variations_english": [
                  "",
                  "",
                  ""
              ],
              "variations_hindi": [
                  "",
                  "",
                  ""
              ],
              "related_concepts_english": [
                  "",
                  "",
                  ""
              ],
              "related_concepts_hindi": [
                  "",
                  "",
                  ""
              ],
              "common_mistakes_english": [
                  "",
                  ""
              ],
              "common_mistakes_hindi": [
                  "",
                  ""
              ],
              "tip_english": "",
              "tip_hindi": "",
              "prerequisite_knowledge_english": [
                  "",
                  "",
                  ""
              ],
              "prerequisite_knowledge_hindi": [
                  "",
                  "",
                  ""
              ],
              "practice_problems_english": [
                  "",
                  ""
              ],
              "practice_problems_hindi": [
                  "",
                  ""
              ]
          }