MemberJanuary 30, 2021 at 11:08 pm
I thought of this problem many years ago but I’ve never been able to come up with a solution, although I feel there ought to be one. Maybe you folks would be interested in giving it a try. It goes like this:
In the 1951 movie When Worlds Collide (as I remember it), a large team works frantically to build a spaceship to escape the Earth before it’s destroyed. When someone realizes that there are more people building the ship than it can carry, it’s decided that a lottery will be held and the winners announced on launch day. When that day comes and the list of winners is posted, a young man finds his name on the list and runs to tell his girlfriend, but when he finds her she’s crying because, tragically, her name isn’t on the list.
The puzzle is this: How could a lottery be held that would avoid situations like that? Can you devise a set of lottery rules that would allow couples, or perhaps even larger groups, to specify in advance that either all of the group or none of the group win, while maintaining exactly the same probability of winning for each individual person, including those who choose not to pair up with anyone?
AdministratorMarch 1, 2021 at 4:16 pm
That’s an interesting question, but I think we need to figure out the exact rules/conditions first. For example, if there is empty space on the plane, does it need to be taken if possible? I feel a cool combinatorial/probability problem can come up from this but we need to set it up properly… For one, you can always split people into N groups based on their preferences and give each group a chance of 1/N but that’s very suboptimal… Do you have something more specific in mind?
MemberMarch 1, 2021 at 11:29 pm
Thanks for the response!
I don’t think we need to figure out the exact rules/conditions first, I’d rather see someone come up with a solution that works in at least some conditions, then take it from there. In other words, in the absence of an outright solution I’m interested in at least seeing an analysis.
Here’s a start: Suppose only singles and couples were allowed. If the young man and his girlfriend were both chosen then they’d both go. If neither were chosen then neither would go. But if one was chosen and the other was not then they’d either both go or both stay, depending upon a coin flip. Would that work?