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This is what I would call an eduacted guess but my answer is 7.
Basically, the first person is going to call out what is the majority color of the hats. There will have to be a majority because there are 9 hats he will see. He may surely. The next person takes one from the majority and says the majority number unless the number is now even. If he says white, he may die , but all the others know exactly how many red and whites there were and therefore can figure out what colour hat they had from knowing if the person behind is alive or dead and the colours ahead.
However, if there are still more reds, the combo can only be either 8 reds; 7 reds, 1 white; 6 reds; 2 white; 5 reds, 3 whites (not including what the 9th person is wearing).
Obviously the worse case scenario is the 6 and 2. The person will say red as that is the majority ahead, if he dies then the person ahead knows one of the whites is gone and that he will see only 1 white ahead. Therefore all the others are likely to say red, meaning only one more will die.
Nope
Man, people are having a hard time with this one.