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: E / इ — *Even and Odd Numbers / सम और विषम संख्या*

    #### 📚 Concept:
    - EN: Even and Odd Numbers  
    - HI: सम और विषम संख्या

    #### 🧠 Type:
    - EN: Even and Odd Numbers  
    - HI: सम और विषम संख्या

    #### 📖 Description:
    - EN: Classifying numbers into even or odd and solving related problem scenarios.  
    - HI: संख्याओं को सम और विषम वर्गीकरण करना एवं संबंधित समस्याएं हल करना।

    #### 📌 Explanation:
    - EN: Even numbers are divisible by 2, odd are not. Their properties help in sequence/series problems and parity checks in problems.  
    - HI: सम संख्याएँ 2 से विभाजित होती हैं, विषम नहीं। इन गुणों का उपयोग श्रेणी/धाराओं और समता जाँच में होता है।

    #### ➗ Formula or Relation:
    - EN: **Even Number = 2n, Odd Number = 2n+1 (n ∈ Integers)**  
    - HI: **सम संख्या = 2n, विषम संख्या = 2n+1 (n सम पूर्णांक)**

    #### 💡 Example Questions:
    **ENGLISH:**
    ['A bus passes every 15 minutes and a train every 20 minutes. If a passenger arrives at a stop randomly between 8 am and 9 am, what is the chance he will catch an even number minute arrival time? Consider even and odd number distributions over time.', 'From a list of 200 consecutive numbers starting from 101, find the count of even numbers. Additionally, if every even number corresponds to shifts working on alternate days, determine how many total shifts are assigned in a month.', 'If the sum of three consecutive even numbers is 72, find the numbers. Explain the approach using properties of even numbers and formulate the expression leading to the solution.']

    **HINDI:**
    ['एक बस हर 15 मिनट में गुजरती है और ट्रेन हर 20 मिनट में। यदि यात्री 8 बजे से 9 बजे के बीच किसी भी समय पहुंचता है, तो संभावना ज्ञात करें कि वह सम संख्या मिनट पर आने वाली बस या ट्रेन को पकड़ सके।', '200 लगातार संख्याओं में से जो 101 से शुरू होती हैं, उनमें कितनी सम संख्याएँ हैं? यदि प्रत्येक सम संख्या वैकल्पिक दिनों में शिफ्ट कार्यों का प्रतिनिधित्व करती है, तो महीने में कुल कितनी शिफ्ट असाइन होंगी? गणना करें।', 'तीन लगातार सम संख्याओं का योग 72 है। उन संख्याओं को खोजें। सम संख्याओं के गुणधर्म का उपयोग करते हुए समाधान 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": [
                  "",
                  ""
              ]
          }