math plus simulation Pattern
Pattern hubs are for building transferable solving frames. Learn the recognition signals first, then drill state definition, update rules, and edge explanation until the pattern feels stable.
Pattern brief
Recognize first
Candidate should show understanding of basic digit operations and how to optimize them.
Solve rhythm
State the active state and invariant first, explain how each update preserves them, then pressure-test with counterexamples.
Most common miss
Misunderstanding the problem and applying unnecessary loops or calculations.
Recognition signals
- Candidate should show understanding of basic digit operations and how to optimize them.
- Look for recognition of number properties like digital roots and their use in optimization.
- Candidate should focus on simulating the candy distribution step by step.
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Misunderstanding the problem and applying unnecessary loops or calculations.
- Misunderstanding the cyclical distribution process and giving candies in the wrong order.
- Failing to correctly simulate the bottle exchange and drinking process.
Recommended Ladder
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