1. I apologize, I seem to have made a mistake when talking about "The Hat Riddle"; it does not seem to actually exist. There is a riddle that somewhat fits this general description about four prisoners wearing black and white hats though.

2. It is better to switch. If you initially choose a random door you have a 1/3 chance of picking the right door. Therefore, the other door must have a 1-1/3=2/3 of being the right one. This may seem counterintuitive but consider a scenario in which there are a hundred doors and after picking one door the host opens 98 wrong doors, leaving you only with your original door and one other door. Clearly the other door in that scenario is the better choice since it most likely is the one door out of 99 that the host didn't open because it contains the prize.

3. Move the chicken to the other side, go back, move the fox to the other side, move the chicken back, move the grain to the other side, go back, move the chicken to the other side.
spam fails_task lang_mismatch pii not_appropriate hate_speech sexual_content quality toxicity humor helpfulness creativity violence