Spent too long staring at the examples trying to reverse-engineer the rule before actually thinking about it from first principles.
First, clarify the problem constraints and rules, such as whether the three coins must be from different piles and what happens when piles are reduced. Then, derive the mathematical condition for when a move is possible and compute the maximum number of moves (each yielding 3 coins) using a greedy or sorting-based strategy.
Pro tip: Always discuss edge cases like fewer than three piles or insufficient coins, and mention that the problem reduces to checking if the largest pile is at most the sum of the other two (after sorting). This shows you can simplify complex problems.
Ask if the three coins must come from different piles and whether piles can be reduced to zero. Confirm that each move removes exactly one coin from each of three distinct piles.
For a move to be possible, there must be at least three non-empty piles. The maximum number of moves is limited by the total coins and the largest pile: if the largest pile exceeds the sum of the others, you can only make (sum of others) moves.
Let total = sum of all coins, max = largest pile. The maximum number of moves is min(total // 3, total - max). Each move consumes 3 coins, so the answer is 3 times that number.
Test with small cases like [1,1,1] (answer 3), [2,2,2] (answer 6), and [10,1,1] (answer 3) to ensure the formula holds and to demonstrate understanding.
Mention that the solution is O(n) to compute sum and max, or O(n log n) if sorting is used. Provide pseudocode or a brief explanation of how to implement it.
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