logic puzzles.txt

Solvable boolean logic puzzles.

1 statement:
A: A							unsolvable

A: !A							paradox

A: A||!A						true (tautology)

A: A&&!A						false (contradiction)


2 statements:
A: true
B: A							true
B: !A							false
B: A||B							true
B: A||!B						true
B: !A||B						unsolvable
B: !A||!B						paradox
B: A&&B							unsolvable
B: A&&!B						paradox
B: !A&&B						false
B: !A&&!B						false

A: false
B: repeat the above ten items but reversing A and !A


A: B
B: A							unsolvable

A: B
B: !A							paradox
(repeat the above two items in reverse for A: !B)

A: A&&B							A is false to avoid paradox below
B: A&&!B						B is false because A is false

A: A||B							A is true to avoid paradox below
B: A||!B						B is true because A is true

Can flip the !s around to reverse the roles of A and B or to make them unequal

A: A||!B						Same as A: !B, B: !A
B: !A||B						A and B are unequal but which is what is unsolvable


3 statements:
A: B
B: C
C: A							unsolvable

A: !B
B: C
C: A							paradox

A: !B
B: !C
C: A							unsolvable

A: !B
B: !C
C: !A							paradox

A: B&&C							false because B and C are exclusive
B: !A							true because A must be false
C: A							false because A must be false

A: B&&C							false because B and C are exclusive
B: C&&!A						false because C is false
C: B&&A							false because A must be false

A: B&&!C						paradox: if A is true B is true and false while C is false and true, if A is false then B is true and C is false which means A is true
B: !A							
C: A							

A: B&&!C						unsolvable: consistent whether A is true or false
B: A							
C: !A							

A: B&&!C						false: if it was true, C is both false and true
B: C&&A							false because A must be false
C: !A							true because A must be false

A: B&&!C						false: if it was true, C would be both false and true
B: A							false because A must be false
C: A							false because A must be false

A: B&&!C						false: if it was true, B would be both true and false
B: !A							true because A must be false
C: !A							true because A must be false

A: B&&!C						false: if it was true, B would be both true and false
B: !A							true because A must be false
C: !A&&!B						false because B must be false




A: C
B: C
C: !A||!B						paradox

A: C							true
B: C							true
C: !A||B						true: if false, contradiction



Generating puzzle:
Method 1: generate a contradiction, then provide an || "something that's true"
Method 2: generate a contradiction, then provide an && "something that's false"
Method 3: generate something that is valid in two states then add a contradiction to one possibility
Method 4: generate a tautological statement

Start with core, then add in some extra statements which branch off.


Core:
if 1 statement, make it a tautology or contradiction about itself
if 2 statements, choose values, decide &&/||, force one with a paradox