The correct answer is 45. Too bad for the everybody knows that the representatives are extremely greedy and smart. If there would have been somebody not so smart in here, things might have been distributed a little bit more evenly. Everybody that gets at least one Raptor will vote yes, because they know they won't get any in the next round if they decline now. You get to this result by starting starting it backwards. In a two colony situation, the first one will take all of the raptors for itself and get them, because there are only 2 of them (50% approval guaranteed). So in a three colony situation the first colony has to provide a distribution to gather a second vote. This is easily achieved by assigning 1 raptor to the last colony, because this colony will get no raptor if it declines the proposition. If you repeat this logic up to 12 colonies you get the following distribution.
Aerilon |
45 |
Aquaria |
0 |
Canceron |
1 |
Caprica |
0 |
Gemenon |
1 |
Leonis |
0 |
Libran |
1 |
Picon |
0 |
Sagittaron |
1 |
Scorpia |
0 |
Tauron |
1 |
Virgon |
0 |