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Ah yes, how about this:
optimal_move = if N ≤ 2: invalid
if N ≤ 4: N-1
if N mod 4 ∈ {1,3}: 2
if N mod 4 ∈ {0,2}: 3
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Ah yes, how about this:
optimal_move = if N ≤ 2: invalid
if N ≤ 4: N-1
if N mod 4 ∈ {1,3}: 2
if N mod 4 ∈ {0,2}: 3
You're on the right track, but the solution is not quite accurate yet.
For example, if N=3, your solution says take 3. But that's rude because you take the last dumpling.
Another example, if N=5, your solution says take 1. But if N=5, you can take 3, then the next person will take 1, leaving the next person with the last dumpling. This maximizes your dumplings without being rude.