> Correct me if I'm wrong, but the game show didn't authorize contestants "to relabel the doors, or" permute the door numbers. So what permits you to do any of this in this solution?
The game show never labeled the doors in the first place. We are the ones labeling the doors, so we are free to label them as we please.
It might be more helpful if you just think of it as something more like "After the contestant picks a door, we label that door 'door 1'." Then we aren't relabeling anything, just flat out saying that no matter which door they choose, we call it door 1.
Moshi
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2021-08-05T04:05:52Z (over 3 years ago)