Implement Open-Ended Questions Logic

[ryanmio]

Implement the game logic for open-ended questions. This includes generating the questions, checking the user's answer, and providing feedback.

Acceptance Criteria:

• Questions should be generated based on the code snippets.
• The user's answer should be checked against the correct answer.
• Feedback should be provided to the user based on their answer.

Files to be used/created:

• backend/firebase_functions/game_logic.js
• frontend/game_mode_selection_ui.js