LLM-based tutors are typically single-turn assistants that lack persistent representations of learner knowledge, making it difficult to provide principled, transparent, and long-term pedagogical support. We introduce IntelliCode, a multi-agent LLM tutoring system built around a centralized, versioned learner state that integrates mastery estimates, misconceptions, review schedules, and engagement signals. A StateGraph Orchestrator coordinates six specialized agents: skill assessment, learner profiling, graduated hinting, curriculum selection, spaced repetition, and engagement monitoring, each operating as a pure transformation over the shared state under a single-writer policy. This architecture enables auditable mastery updates, proficiency-aware hints, dependency-aware curriculum adaptation, and safety-aligned prompting. The demo showcases an end-to-end tutoring workflow: a learner attempts a DSA problem, receives a conceptual hint when stuck, submits a corrected solution, and immediately sees mastery updates and a personalized review interval. We report validation results with simulated learners, showing stable state updates, improved task success with graduated hints, and diverse curriculum coverage. IntelliCode demonstrates how persistent learner modeling, orchestrated multi-agent reasoning, and principled instructional design can be combined to produce transparent and reliable LLM-driven tutoring.