Answer: $$97,0,1,0,2.$$ We reason backwards. With a pirate, he keeps the 100 coins: $$100.$$ With two pirates, more than half of the votes are needed. That is, 2 votes are needed. The proposer needs the other pirate to vote in favor. If the proposer dies, the other pirate is left alone and gets 100 coins. Therefore, for him to accept, we must offer him 100. The distribution is: $$0,100.$$ With three pirates, 2 votes are needed. If the first dies, there would be the case of two pirates: $$0,100.$$ The second pirate would receive 0 and the third would receive 100. The proposer buys the second with 1 coin and keeps 99: $$99,1,0.$$ With four pirates, 3 votes are needed. If the first one dies, it would be the case of three pirates: $$99,1,0.$$ The second, third and fourth pirates would respectively receive 99, 1 and 0. The proposer already has his own vote, but needs two more. He can't buy the second one cheaply, so he buys the third one with 2 coins and the fourth one with 1: $$97,0,2,1.$$ With five pirates, 3 votes are needed. If the first one dies, there would be the case of four pirates: $$97,0,2,1.$$ The second, third, fourth and fifth pirates would respectively receive 97, 0, 2 and 1. The proposer already has his vote and needs two more votes. Buy from the cheapest: to the third pirate, who would receive 0, you offer 1; To the fifth pirate, who would receive 1, he offers 2. This is how you keep 97 coins: $$97,0,1,0,2.$$ That is the optimal distribution under a strict majority.