♟️ Strategy & Optimization

Find the best move, the fewest steps, the smartest plan

🎯 Minimum and maximum

Many competition problems ask for the smallest or largest value possible. Try extreme cases first.

If asked for the minimum number of moves, think about what MUST happen — the answer is at least that many.

Test the edges What happens if you push something to its limit? That often reveals the answer.

Sometimes the end state is clearer than the start. Start from the goal and undo each step.

Example: "After doubling and adding 3, the result is 17"

The original number was 7. It's much easier than solving an equation!

In take-away games, look for a winning position you can always reach.

If you can take 1–3 objects and the person taking the last one loses, then leaving your opponent with 1 is a win
Work backwards: leave them at 1, 5, 9, 13... (multiples of 4, plus 1)

Find the pattern, then always move to stay ahead!

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