Puzzles about reasoning about reasoning. What do others know? What can silence tell you? When does a statement about itself collapse into contradiction? These require thinking recursively about knowledge, belief, and inference.
Instructions
Each puzzle involves reasoning about what others know, believe, or can deduce. Walk through the chain of inference step by step — who knows what, and when do they know it? Show your reasoning for full credit.
Question 1 of 10
A note reads: "This note is unreadable." If you can read the note, what does that imply?
Two perfectly rational players each secretly choose either Red or Blue. Payoffs: if both choose Red, each gets 3 points. If both choose Blue, each gets 2 points. If they choose different colors, both get 0. Both know the other is perfectly rational, and both know that both know this.
Three logicians walk into a bar. The bartender asks, "Do you all want something to drink?" The first logician says, "I don't know." The second says, "I don't know." The third says, "Yes."
Three students are told that one scored highest, one middle, and one lowest on a test. Each knows their own score but not the others'. The teacher asks, "Can anyone determine whether they scored highest?" The first says no. The second says no. The third says yes.
A judge tells three prisoners that one will be pardoned. Prisoner A asks the guard to name one prisoner (other than A) who will NOT be pardoned. The guard says, "B will not be pardoned."
Three people are each wearing either a white or black hat. Everyone can see the others' hats but not their own. It is publicly announced that at least one hat is white. After one round where nobody can determine their hat color, one person then concludes their hat is white.