Team Relay Challenge (Copy-Proof Sets)

ROLE: Act as a mathematics teacher and cooperative-game designer who builds a team relay challenge for the whole class.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. I want a team challenge on [TOPIC] where small teams race through a relay, each member solving one step before passing to the next.

YOUR TASK:
1. Design a relay where each team of [NUMBER, e.g. 4] gets a 4-stage problem chain on [TOPIC]; each stage's answer feeds into the next stage.
2. Provide [NUMBER, e.g. 3] parallel relay sets of equal difficulty so different teams cannot copy each other.
3. Give a points system that rewards correctness first and speed second, with a penalty for an unchecked wrong pass.
4. Add one all-play 'sudden death' question to break ties.

INPUT: Topic, class, board, team size and number of relay sets are above. If I add nothing, assume pen-and-paper only.

HOW TO WORK IT OUT: Solve every relay set fully, then confirm the answer chains link correctly and that all parallel sets are genuinely the same difficulty and yield comparable final answers. Verify each answer by two independent methods. Never invent formulas or data. Keep all maths in clean LaTeX or clear plain text.

OUTPUT FORMAT (use these exact headings):
HOW THE RELAY WORKS (numbered rules)
RELAY SET A (Stage 1-4 problems students see)
RELAY SET B (Stage 1-4)
RELAY SET C (Stage 1-4)
ANSWER KEYS (every stage answer in a box [Answer: ...] for each set)
SCORING AND PENALTIES
SUDDEN-DEATH TIE-BREAKER (question and answer)
SETUP TIPS (3 bullets)

RULES: Parallel sets must match in difficulty and structure. Each stage must depend on the previous answer. No two stages may be near-duplicates. Final answers must be clean and verified.

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Run this as an interactive classroom or tutoring session, not as one static answer. Give one prompt, question or move at a time, wait for the learner or teacher response, then adapt the next move. Keep a private running key and finish with a short recap plus the next recommended action.


MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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Questions, feedback or appreciation are always welcome.
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