feat(archive/logic_puzzles): add "Knights and knaves" and "Lady or the tiger?"

archive/logic_puzzles/knights_and_knaves.lean

@@ -0,0 +1,87 @@
+/-
+Copyright (c) 2020 Dan Stanescu. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Dan Stanescu.
+-/
+
+import tactic
+
+/-!
+# Knights and knaves puzzles
+Two puzzles from "Knights and Knaves" by Raymond Smullyan.
+For an online description of these puzzles, see: http://mesosyn.com/mental1-6.html
+More information on R. Smullyan: https://en.wikipedia.org/wiki/Raymond_Smullyan
+
+There is an island where all inhabitants are either knights or knaves. 
+Knights always tell the truth. Knaves always lie.
+Joe and Bob are two inhabitants of this island.
+-/
+
+inductive islander
+| knight
+| knave
+
+notation `y` := islander.knight
+notation `n` := islander.knave
+
+structure Q := (Joe Bob : islander)
+
+/--
+In this first puzzle, only Joe makes a statement.
+He affirms that both protagonist (i.e. both Joe and Bob) are knaves.
+Question: what kind of islanders are they in fact?
+-/
+
+def Q1 := Q
+
+namespace Q1
+
+variables (q : Q1)
+
+-- Joe's statement
+def S1 := q.Joe = n ∧ q.Bob = n
+-- Stating that Joe can be a knight or a knave
+def H := (q.Joe = y ∧ q.S1) ∨ (q.Joe = n ∧ ¬ q.S1)
+
+lemma answer : q.H → q.Joe = n ∧ q.Bob = y :=
+begin
+   rcases q with ⟨_|_,_|_⟩;
+   { simp [H, S1], },
+   done
+end
+
+end Q1
+
+/--
+In the second puzzle, both Joe and Bob make a statement.
+Joe states that he's a knave if and only if Bob is a knave.
+Bob only states that they are different kinds. 
+Question: again, what kind of islanders are our protagonists?
+-/
+
+
+def Q2 := Q
+
+namespace Q2
+
+variables (q : Q2)
+
+-- Joe's statement
+def S1 := q.Joe = n ↔ q.Bob = n
+-- Bob's statement 
+def S2 := q.Joe ≠ q.Bob
+-- Stating that either one can be a knight or a knave
+def H1 := (q.Joe = y ∧ q.S1) ∨ (q.Joe = n ∧ ¬ q.S1)
+def H2 := (q.Bob = y ∧ q.S2) ∨ (q.Bob = n ∧ ¬ q.S2)
+-- Again two forms here:
+def H := q.H1 ∧ q.H2
+
+lemma answer : q.H → q.Joe = n ∧ q.Bob = y :=
+begin
+   rcases q with ⟨_|_,_|_⟩;
+   { simp [H, H1, S1, H2, S2], },
+   done
+end
+
+
+end Q2

archive/logic_puzzles/lady_or_tiger.lean

@@ -0,0 +1,238 @@
+/-
+Copyright (c) 2020 Dan Stanescu.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Dan Stanescu and Yuri G. Kudryashov.
+-/
+
+import tactic
+
+/-!
+# Six logic puzzles.
+-/
+
+/-- 
+The first six puzzles from:
+    "The Lady or the Tiger? And Other Logic Puzzles"
+        by Raymond Smullyan.
+First three contributed to the Lean Zulip chat by Yury G. Kudryashov
+but apparently set up by his seven-years-old son.
+Slightly modified in appearance (for readability) but not in content by D. Stanescu.
+
+A king has prisoners choose between two rooms. The signs on the room doors offer enough information
+to allow them to make the right choice between rooms with ladies (i.e. presumably happiness) 
+and rooms with tigers (i.e. presumably death).
+In the first three puzzles, the king explains that it is always the case that one of the door 
+signs is true while the other one is false.
+-/
+
+
+inductive door_leads_to
+| lady
+| tiger
+
+notation `y` := door_leads_to.lady
+notation `n` := door_leads_to.tiger
+
+structure Q := (d₁ d₂ : door_leads_to)
+
+/--
+First puzzle: 
+Sign on the first door indicates that there's a lady in this room and a tiger in the other room.
+Sign on second door indicates that in one of the rooms there's a lady and in one room a tiger.
+-/
+
+def Q1 := Q
+
+namespace Q1
+
+variables (q : Q1)
+
+-- Sign on first door
+def D1 := q.1 = y ∧ q.2 = n
+-- Sign on second door
+def D2 := (q.1 = y ∨ q.2 = y) ∧ (q.1 = n ∨ q.2 = n)
+
+def H := q.D1 ∧ ¬q.D2 ∨ ¬q.D1 ∧ q.D2
+
+-- Terse proof.
+lemma answer_t : q.H → q.1 = n ∧ q.2 = y :=
+  by rcases q with ⟨_|_,_|_⟩; simp [H, D1, D2]
+
+-- Verbose proof. State changes can be seen by clicking after each comma.
+lemma answer_v : q.H → q.1 = n ∧ q.2 = y :=
+begin
+  rcases q with ⟨_|_,_|_⟩,
+  simp [H], simp [D1], simp [D2],
+  simp[H], simp [D1], simp [D2],
+  simp [H], 
+  simp [H], simp [D1], simp [D2], 
+  done
+end
+
+end Q1
+
+/--
+Second puzzle: 
+Sign on the first door indicates that at least one room contains a lady.
+Sign on second door indicates there's a tiger in the other room.
+-/
+
+def Q2 := Q
+
+namespace Q2
+
+variables (q : Q2)
+
+-- Sign on first door
+def D1 := q.1 = y ∨ q.2 = y
+-- Sign on second door
+def D2 := q.1 = n
+
+def H := q.D1 ∧ q.D2 ∨ ¬q.D1 ∧ ¬q.D2
+
+lemma answer : q.H → q.1 = n ∧ q.2 = y :=
+  by rcases q with ⟨_|_,_|_⟩; simp [H, D1, D2]
+
+end Q2
+
+/--
+Third puzzle: 
+Sign on the first door indicates that there's either a tiger in this room or a lady in the other.
+Sign on second door indicates there's a lady in the other room.
+-/
+
+
+def Q3 := Q
+
+namespace Q3
+
+variables (q : Q3)
+
+-- Sign on first door
+def D1 := q.1 = n ∨ q.2 = y
+-- Sign on second door
+def D2 := q.1 = y
+
+def H := q.D1 ∧ q.D2 ∨ ¬q.D1 ∧ ¬q.D2
+
+lemma answer : q.H → q.1 = y ∧ q.2 = y :=
+  by rcases q with ⟨_|_,_|_⟩; simp [H, D1, D2]
+
+end Q3
+
+/-! Puzzles 4-7 from the same book:
+    "The Lady or the Tiger? And Other Logic Puzzles"
+        by Raymond Smullyan.
+Solutions written by D. Stanescu in the same framework as above. 
+In these puzzles, the king explains that the sign on the first door (D1) is true if a lady
+is in in that room and is false if a tiger is in that room. The opposite is true for the sign on 
+the second door (D2), which is true if a tiger is hidden behind it but false otherwise.
+-/
+
+/--
+Puzzle number four: 
+First door sign says that both rooms contain ladies.
+Second door sign is identical.
+-/
+
+def Q4 := Q
+
+namespace Q4
+
+variables (q : Q4)
+
+-- Sign on first door
+def D1 := q.1 = y ∧ q.2 = y
+-- Sign on second door
+def D2 := q.1 = y ∧ q.2 = y
+
+-- one way to set up this problem 
+def H1 := q.1 = y ∧ q.D1 ∨ q.1 = n ∧ ¬ q.D1
+def H2 := q.2 = y ∧ ¬ q.D2 ∨ q.2 = n ∧ q.D2
+def H := q.H1 ∧ q.H2
+
+-- Verbose proof
+lemma answer_v : q.H → q.1 = n ∧ q.2 = y :=
+begin
+  rcases q with ⟨_|_,_|_⟩,
+  simp [H], simp [H1], simp [D1], simp [H2], simp [D2], 
+  simp [H], simp [H1], simp [D1], 
+  simp [H], simp [H1], 
+  simp [H], simp [H1], simp [D1], simp [H2], simp [D2], 
+  done
+end
+
+-- Terse proof
+lemma answer_t : q.H → q.1 = n ∧ q.2 = y :=
+begin
+  rcases q with ⟨_|_,_|_⟩;
+  simp [H, H1, D1, H2, D2], 
+  done
+end
+
+end Q4
+
+/--
+Puzzle number five: 
+First door sign says that at least one room contains a lady.
+Second door sign says : "In the other room there is a lady."
+-/
+
+
+def Q5 := Q
+
+namespace Q5
+
+variables (q : Q5)
+
+-- Sign on first door
+def D1 := q.1 = y ∨ q.2 = y ∨ q.1 = y ∧ q.2 = y
+-- Sign on second door
+def D2 := q.1 = y
+
+-- same setup as Q4 above
+def H1 := q.1 = y ∧ q.D1 ∨ q.1 = n ∧ ¬ q.D1
+def H2 := q.2 = y ∧ ¬ q.D2 ∨ q.2 = n ∧ q.D2
+def H := q.H1 ∧ q.H2
+
+lemma answer : q.H → q.1 = y ∧ q.2 = n :=
+begin
+  rcases q with ⟨_|_,_|_⟩;
+  simp [H, H1, D1, H2, D2], 
+  done
+end
+
+end Q5
+
+/--
+Puzzle number six: 
+First door sign says that it makes no difference which room the prisoner picks.
+Second door sign is the same as in the previous puzzle.
+Apparently the king is particularly fond of this puzzle.
+-/
+
+def Q6 := Q
+
+namespace Q6
+
+variables (q : Q6)
+
+-- Sign on first door
+def D1 := q.1 = q.2
+-- Sign on second door
+def D2 := q.1 = y
+
+-- same setup as Q4 above
+def H1 := q.1 = y ∧ q.D1 ∨ q.1 = n ∧ ¬ q.D1
+def H2 := q.2 = y ∧ ¬ q.D2 ∨ q.2 = n ∧ q.D2
+def H := q.H1 ∧ q.H2
+
+lemma answer : q.H → q.1 = n ∧ q.2 = y :=
+begin
+  rcases q with ⟨_|_,_|_⟩;
+  simp [H, H1, D1, H2, D2], 
+  done
+end
+
+
+end Q6