by bribing 100 pirates with one gold coin each. This seems most likely to work by bribing odd-numbered pirates optionally including #202, who will get nothing from #203. However, it may also be possible to bribe others instead as they only have a 100/101 chance of being offered a gold coin by pirate #202. With 205 pirates, all pirates bar #205 prefer to kill #205 unless given gold, so #205 is doomed as captain. Similarly with 206 or 207 pirates, only votes of #205 to #206/7 are secured without gold which is insufficient votes, so #206 and #207 are also doomed. For 208 pirates, the votes of self-preservation from #205, #206, and #207 without any gold are enough to allow #208 to reach 104 votes and survive. In general, if G is the number of gold pieces and N (> 2G) is the number of pirates, then All pirates whose number is less than or equal to 2G + M will survive, where M is the highest power of 2 that does not exceed N – 2G. Any pirates whose number exceeds 2G + M will die. Any pirate whose number is greater than 2G + M/2 will receive no gold. There is no unique solution as to who gets one gold coin and who does not if the number of pirates is 2G+2 or greater. A simple solution dishes out one gold to the odd or even pirates up to 2G depending whether M is an even or odd power of 2. Another way to see this is to realize that every pirate M will have the vote of all the pirates from M/2 + 1 to M out of self preservation since their survival is secured only with the survival of the pirate M. Because the highest ranking pirate can break the tie, the captain only needs the votes of half of the pirates over 2G, which only happens each time (2G + a Power of 2) is reached. For instance, with 100 gold pieces and 500 pirates, pirates #500 through #457 die, and then #456 survives (as 456 = 200 + 28) as they have the 128 guaranteed self-preservation votes of pirates #329 through #456, plus 100 votes from the pirates they bribe, making up the 228 votes that they needs. The numbers of pirates past #200 who can guarantee their survival as captain with 100 gold