In that case, the 202th pirate will also survive. The question says that at least 50% of the vote is needed. So if N=202, the will get the approval from pirate 2, 4, 6, ... , 200, plus himself. Which is 50%

I agree that 202 survives, I missed this point. In fact it doesn't stop at 202..pls see below

"In general, C is the maximum number of coins, then no pirates older than (2C+1) will survive."

Can you explain why (and why those pirates won't simply instead vote in favor of any proposal?)

You are 50% right, if you follow my assumption. If you follow the other assumption (which goodstudent & marilapi is following), all the odd ones for N > 202 will get killed. All the even ones survives for N > 202. Please refer to case (6) below, all the way at the bottom. Pls lemme know if I missed any more points. This is getting more and more complex now..I might have missed some cases.

Updated cases:

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Case (1): For 4 < N < 200

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P(N) gets {100 - (N/2)} coins. {N/2 == only the integral part}

P(N-1) gets nothing

Among P(1) to P(N-2), any {N/2} of them get 1 coin each.

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Case (2): N >= 200

P(N) gets 0 coins if N is odd, 1 coin if N is even.

Among P(k), { (0 < k < 200)&&( k != (N-1)) OR ((N - 1) > k > 199)&&(k is even number)

99 (If N is even) or 100 (If N is odd) of them will get one coin each.

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This covers all cases, but I have explained few cases below.

Examples:

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Case (3): N = 201

P(200) & P(201) gets nothing.

Among P(1) to P(199), any 100 of them get 1 coin each.

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Case (4) N = 202

P(202) gets one coin

Among P(1) to P(200), any 99 of them get 1 coin each.

P(201) will vote (As per my assumption, he won't get any coins anyway)

Hence P(202) will get 99 + P(202) + P(201) = 101 votes

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Case 5: N = 203

P(N> 200) gets no coins

Among P(1) to P(200), any 100 of them get 1 coin each.

Here P(203) will survive according to my assumption (since P(201) will vote for him in spite of not getting any coins), else he will be killed.

If he is killed Case (4) will come into effect.

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Case 6: N = 203, According to the assumption which goodstudent & marilapi is following:

P(203) MAY get killed.

Since he can only get 101 votes. P(201) need not vote for him without a coin, and he can get votes of 100 odd numbered pirates out of 101 odd numbered pirates other than himself.

Similarly all odd ones may get killed, even ones survives for N >=203.