In this scenario, how can we devise a strategy to maximize the success rate of the entire group?
💡 Model Answer
The optimal strategy uses a parity or modulo system. The first person announces a value (e.g., "red" for even parity of red hats, "blue" for odd). This announcement encodes the parity of all hats ahead. Each subsequent person counts the number of red hats they see and subtracts the parity announced by the first person and the guesses of those ahead of them. The difference tells them their own color. This method ensures that every person after the first can deduce their hat color exactly, guaranteeing 99 correct guesses out of 100.
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